See the list of Calculus step-by-step solutions available
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[Solved] Find f(2),f(3),f(4),f(5) if f(n) is defined recursively by f(0)=0,f(1)=1,f(n+1)=f(n)+2f(n-1)+1 for #24975
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[Solved] Solve the following recurrence relations together with the initial conditions given. {a_n}=2{{a}_{ #24981
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[Solved] Solve the following y'= sin t+{e^{-t}}, y(0)=0 #24989
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Solution: Solve the following y'=1+(y)/(t), y(1)=2 #24990
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[Solution] Solve the following y'=-ty+(4t)/(y), y(0)=1 #24991
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[Solved] Solve the following y'=(1)/(t(y^2+y)), y(1) = -2 #24992
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[Solved] Solve the following y'=-50y+ sin t, y(0)=0 #24993
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[Solved] Use the Trapezoidal estimate with n = 10 to estimate ∫_0^2{{e^{-x^2}}dx}. #25067
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[Solution] Use Simpson’s Rule with n = 6 to estimate ∫_1^3{√{ln x}dx} #25068
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Solution: Find the interval of convergence of the power series: ∑limits_{n=1}^{∞ }{{{(x-3)}^n}(1)/(n #25086
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(Solved) Find the Maclaurin series for the function f(x)= arctan x. #25087
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[Solved] Find the distance between each pair of points. (-3, 0) and (4, 0) #25131
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[Solution] Q1: Determine the derivatives of: a) (d)/(dx)({e^{-4x}} sin 7x) b) (d)/(dx)((ln (x+1))/( cos 3x #25138
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(See Solution) Q3: If x=3{t^2}- t and y=8t-5 find (dy)/(dx) when t=1 #25139
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(Solved) Q1: The displacement S in m of an object from a fixed point at time t sec is given by the equation: #25140
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[Solved] Q2: The time period (T) for an oscillating mass (m) on a spring with a spring constant (k) is given #25141
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(Solved) Q3: Find the second derivative of y=ln (x^2-3) #25142
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[Solved] Q4: Find (d)/(dx)({{ sin }^{-1}}5x^2) #25143
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[Solved] Q5: Show that (d)/(dx)({{ sin h }^{-1}}(x)/(a))=(1)/(√{x^2+{a^2)}} and find its ({d^2}y)/(dx^2 #25144
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Solution: Q1: Determine (using the method of integration by parts) ∫_{(-π )/(2)}^{(π )/(2)}{x^2 sin #25145
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[Solution] Q2: Determine (using the substitution u=4x^2-1) ∫{(2x)/(√{4x^2-1)}.dx} #25146
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(See Solution) Q3: Determine (by ∂ fractions) ∫{(11-3x)/((x^2+2x-3)).dx} #25147
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[Solved] Q1: Find the volume of the solid of revolution produced when the function y = x^2 + 4 is rotated one #25148
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[Solved] Q2: Find the co-ordinates of the centroid of the area lying between the curve y = x(4 - x) and the x #25149
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[Solved] Q3: Find the position of the centroid of the solid generated by rotating the function y = 1/2x^2 abo #25150
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[Solved] Consider the double integral over a region a. Describe the region by words and by #25343
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[Solution] Set up a triple integral in rectangular coordinates that gives the volume of the ellipsoid . D #25344
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[Solved] Let be a region bounded by the lines. Find the following integral: #25345
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[Solution] For each point, given either in cylindrical or spherical coordinates, find its rectangular coordinat #25346
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Solution: Charge is distributed over a triangular region with vertices at so that the charge density at a po #25347
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Solution: Using triple integrals, find the volume of the conic solid bounded by the plane and the cone z . No #25348
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Solution: Use the change of variables to find a formula for the volume of the ellipsoid #25349
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(Solved) Let the vector field and the plane curve be given as It can be shown by direct calculations that #25350
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[Solution] Find the line integral , where #25351
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[Solution] A moving object’s trajectory in a magnetic field is the circular helix . Determine the amount of wor #25352
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Solution: Consider the vector field and the triangle with vertices and which as a plane curve has a counter-c #25353
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(See Solution) We want to calculate the line integralwhere and is the boundary of the region between the parabol #25354
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[Solution] Consider the space between the upper part of the sphere and the vertical cylinder Write a descript #25355
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Solution: In Example 7.3.5 the MSE of the Bayes estimator, B, of a success probability was calculated (the #25357
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[Solved] Here, the LRT alluded to in Example 8.2.9will be derived. Suppose that we observe m iid Bernoulli #25359
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Solution: In the following, find the pdf of Y and show that the pdf integrates to 1. (c) #25374
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[Solution] Let have the standard normal pdf, (a) Find directly, then by using the pdf of from Example 2. #25375
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[Solution] Let have the pdf . (a) Verify that is a pdf. (b) Find and Var . #25376
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[Solved] Let be iid with pdf . (a) Find the MLE of , and show that its variance ? 0 as n ? ?. (b) #25381
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[Solution] Given y = f(x) = x^2 + 2x +3 a) Use the definitional formula given below to find the deriv #25403
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[Solution] Given, y = f(x) = 2 x3 - 3x^2 + 4x +5 a) Use the Power function to find derivative of the #25404
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(Solved) A ball is thrown straight up in the air with an initial velocity of 64 feet per second (ft/sec). A #25494
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[Solution] For a t-curve with df=8, find each t-value and illustrate your results graphically. a. The t-valu #25528
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(Solved) In a place of business with 400 administrative workers and 300 engineering workers you want to now w #25642
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(Solved) Differentiate: f(x)=(x+1)/(2x^2+2x+3) #26164
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(Solved) Find the derivative of f(x)=5/4{{x}^{4/5}} #26166
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[Solution] Differentiate: f(x)=(5)/(x^3)-(2)/(x^2)-(1)/(x)+200 #26167
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Solution: Find the slope of an equation of the tangent line to the graph of the function f at the specifi #26168
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(Solved) A manufacturer of tennis rackets finds that the total cost C(x) in dollars of manufacturing x racket #26169
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(Solved) Find the derivative f(x)={e^{x^2-1}} #26170
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[Solved] Find the derivative f(x)={e^{(1)/(2x)}} #26171
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(See Solution) Find the derivative f(x)=(3ln x)/(x^2) #26172
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(See Solution) Find the derivative of f(x)=ln {{(x^3-3)}^4} #26173
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(See Solution) Resale Value. A certain piece of machinery was purchased 3 yr ago by Garland Mills for $500,000. Its #26175
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Solution: Evaluate the definite integral ∫_1^3{{{(2x-1)}^{5/2}}dx} #26179
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(See Solution) Find the following integral ∫{(3x^2+2)/({{(x^3+2x))^2}}dx} #26180
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[Solved] Find the following integral ∫{(x^2)/(√{x^3-1)}dx} #26181
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[Solution] Find the following integral ∫{({{t}^{3/2}}+2{{t}^{1/2}}-4{{t}^{-1/2}})dt} #26182
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[Solved] Find the following integral ∫{(x^4-1)/(x^2)dx} #26183
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[Solved] The management of Ditton Industries has determined that the daily marginal revenue function associat #26184
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(See Solution) Tempco Electronics, a division of Tempco Toys, manufactures an electronic football game. An efficien #26185
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Solution: The increase in carbon dioxide (CO2) in the atmosphere is a major cause of global warming. Using dat #26186
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(Solved) Find (d)/(dx)({{ sin }^{-1}}5x^2) Show steps!!! #26279
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[Solution] Find the volume of the solid of revolution produced when the function y =x^2 + 4 is rotated one revo #26280
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Solution: Average rate of change. Instantaneous rate of change (1st derivative). Suppose that the function f(x #26298
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Solution: The following integrals need to be evaluated: #26355
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(See Solution) Is this integral convergent or divergent? If convergent, what is its value? #26356
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(See Solution) What is the length of the curve defined by the following: #26357
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[Solved] The following two expressions are sequences. Are they convergent or divergent? If convergent, what i #26358
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[Solution] The following four expressions are series. Are they convergent or divergent? Please indicate the tes #26359
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[Solution] Find the values of x for which the following series converges. Check endpoints. #26360
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[Solution] For the following, find the first four terms of the Taylor series. #26361
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[Solved] Solve the following two differential equations. #26362
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(See Solution) Solve the following initial-value problem. #26364
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[Solved] Find the general solution of the nonhomogeneous differential equation using the method of undetermin #26365
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[Solution] As the manager of an 80-unit motel you know that all units are occupied when you charge $60 a day pe #26629
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Solution: Determine the radius and interval of convergence. ∑limits_{k=0}^{∞ }{(k)/({{2)^k}}{{x}^k #26634
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(See Solution) Determine the radius and interval of convergence. ∑limits_{k=4}^{∞ }{(1)/({k^2)}{{(3x+2) #26635
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[Solution] Determine the radius and interval of convergence. ∑limits_{k=1}^{∞ }{({{(-1)}^k})/(&radi #26636
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[Solution] Determine the radius and interval of convergence. ∑limits_{k=2}^{∞ }{({{(k!)}^2})/((2k)! #26637
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[Solved] Determine the interval of convergence and the function to which the given power series converges. #26639
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Solution: Find a power series representation of f(x) about c = 0 (refer to example 6.6). Also, determine the r #26640
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(See Solution) Find a power series representation of f(x) about c = 0 (refer to example 6.6). Also, determine the r #26641
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Solution: Find the Maclaurin series (i.e., Taylor series about c = 0) and its interval of convergence. f(x)= #26642
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[Solution] Find the Maclaurin series (i.e., Taylor series about c = 0) and its interval of convergence. f(x)= #26643
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[Solved] Find the Taylor series about the indicated center, and determine the interval of convergence. f(x) #26644
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[Solved] Find the Taylor series about the indicated center, and determine the interval of convergence. f(x) #26645
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Solution: Prove that the Taylor series converges to f(x) by showing that {R_n}(x)→ 0 asn→ ∞ . #26646
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[Solved] Prove that the Taylor series converges to f(x) by showing that {R_n}(x)→ 0 asn→ ∞ . #26647
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[Solution] Use a known Taylor series to find the Taylor series about c = 0 for the given function, and find its #26648
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[Solution] Use an appropriate Taylor series to approximate the given value, accurate to within {{10}^{-11}}. #26650
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[Solved] Use a known Taylor series to conjecture the value of the limit. {x→ 0} lim ( sin x^2-x^2)/({x^ #26651
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[Solved] Use a known Taylor series to conjecture the value of the limit. {x→ 0} lim ({e^{-2x}}-1)/(x) #26652
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[Solution] Use a known Taylor polynomial with n nonzero terms to estimate the value of the integral. ∫_0 #26653
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Solution: Use a known Taylor polynomial with n nonzero terms to estimate the value of the integral. ∫_0^ #26654
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[Solution] Use the Binomial Theorem to find the first five terms of the Maclaurin series. f(x)=√[3]{1+2 #26655
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[Solved] Find the volume of the solid with cross-sectional area A(x). A(x)=10{e^{0.01x}},0≤ x≤ 10 #26656
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