Homeworks 1. When a eircular plate of metal is heated in an oven its radius increases at a rate of 0.01 cm/min. At what rate is the plate's area increasing when its radius is 50 cm.

Q: + 0o Consider the improper integral dx. What will be an appropriate solution and answer? x2+ 2x+2 A ...

A: We have to find value of given improper Integral.

Q: Question 14 3r dx be given. If u=e+2, then the resulting integral is ex+2 du. Compute f (3). Let A n...

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Q: A partide moves according to a law of motion s- ft), tza, where t is measured in seconds and s in fe...

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Q: tan (In |4x²|) (In |(2x)^|)|+C. what is b? The integral of -dx is b In cos

A: Given: ∫tanln4x2xdx Integrate the equation we get, Consider, u=ln4x2 du=2xdx Substitute in integral ...

Q: Find the nth Maclaurin polynomial for the function. 2x - 2 f(x) = n = 4 X +1' Pa(x) %3D

A: Maclaurin series is given by f(x)=f(0)+xf'(0)+x22!f''(0)+x33!f'''(0)+x44!fiv(0)+.... Given f(x)=2x-2...

Q: 8 プ+5

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Q: 5. Find the centroid of the solid formed by revolving the area between the curves: y? = x and y = 2 ...

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Q: Watch the video on partial fractions decomposition with linear factors before answering the question...

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Q: 8. What is de x2+1

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Q: DA farmer wanted to plant six different crops in a rectangular field. To protect it from animals tha...

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Q: Is the given series divergent or convergent? +oo 1 Σ 4n2 - 8n +3 -

A: Limit  Comparision Test :Suppose ∑an and ∑ bn are two positive term series and                limn→∞...

Q: Consider -dx. Using u-substitution and transformation of integrand, then the power formula applies; ...

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Q: Let f(x) = 7x2(x – 11) + 12. Find the critical points c that correspond to local minima.

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Q: Situation 1: Find the area bounded by the curve x^2 = y + 2 and the line x + y = 0 1. Using Simpson'...

A:   A=∫-21 (-x-x2+2) dxA=[2x-x22-x33]-21 A=2(1+2)-12+2-13-83 A=112 A=5.5 square units

Q: Write the first five terms of the sequence, give the exact answer: +00 n+ 19 n=1 Determine whether t...

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Q: 4. f(x) = (Vx)(x² – 2x) %3D 5. y = (x + i)(x² – 1) %3D

A: derivative

Q: Problem Set A (1) For the function f(x)=1- 1x+2 find the following: (i) f(-x) (ii) f(x +k)

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Q: The differential equation x*(x – 2)²y" + 3(x – 2)y' + y = 0, as the singular points at x = 0 and x =...

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Q: Question 21 sin 3x Given: dxWhat is the appropriate formula to find the integral? cos2 (3x) (4- 3 se...

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Q: Let F = %3| Use Stokes' Theorem to evaluate curlF · dS , where S is the hemisphere x? + y? + z² = 1...

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Q: 1. Consider the relation R1: R2 - R such that (r1, y1)R1 (x2, y2) if and only if both points are on ...

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Q: dy of the function y = sec dx (1- Find the derivative + V4 + sin-'(4 + x²) l4+ sin- (4+x²)) tan(1 + ...

A: Topic:- derivatives

Q: Estimate the maximum volume of a conical pile of road salt that can be stored on an area in the shap...

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Q: Watch the introduction to partial fractions video 2 and the video on repeated linear factors e befor...

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Q: Answer the question below: Given: Let h(x, y) = In(xy² + 3x). Suppose k = h(x, y), where x = a² + b*...

A: Given K=h(x,y)=ln(xy2+3x)where x=a2+b4 and y=a2b6+3a  

Q: Given: -dx. Using u-substitution and transformation of integrand, what is u and du? 3Vx - 2x A) u = ...

A: The given integral is 5/[3√x -2x].

Q: dx J. (3+x²)$/z

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Q: Watch the video on partial fractions with a repeated irreducible quadratic factor e and thevideo on ...

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Q: 2. What is the impact propensity? Explain what this means in words. 3. What is the long run multipli...

A: Answer is in step 2.

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

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Q: Evaluate the integral / V4x4 - 12r? +7 xdx A - {(2x?-3) /4x4– 12x?+7 - 2 In |2x?– 3 + V4x4 - 12x2+7|...

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (-1)*+'k! Σ (2...

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Q: Compute the following limits, if possible. You may use L'Hospital's (Bernoulli's) rule if it applies...

A: We need to find limit.

Q: 1.3(5x - 2)dr Sr -4x+ 3

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Q: /atch the video on the improper integral 1/x^2 2 and the video on the nproper integral 1/x 2 before ...

A: We use the formula integration of ex dx=ex.

Q: An open box is to be constructed so that the length of the base is 3 times larger than the width of ...

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: We know that the Taylor series is given byf(x)=∑n=0∞fn(c)n!(x-c)nHere we need to find the Taylor ser...

Q: Calculate F. dS where F = (3xy°, xe", zª) S is the surface of the solid bounded by the cylinder y? +...

A: Let's find. 

Q: Given: 5x2 tan ( 3x) dx. If u=3x³, then the resulting integral is Jf(u) du. Find. 4

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Q: ladder 10 ft long rests against a vertical wall, If the bottom of the ladder slides away from the wa...

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Q: O : (2r-3)/ar- 12x²+ 7 – 2 im |2x*-3 + Vart- 12r²4 7|} +C V4r4– 12r2+7|}

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Q: B. Prove that the given equation is a solution to the given DE: 1. = C,e3* + Cze2* + Cze* ; y"- 6y" ...

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Q: The diagram below shows points P, Q and R. The coordinates of the points are given by P (7.),qs Q(5,...

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Q: 10" (2n)!

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Q: dx Given: 7-ge-2x. Using u-substitution and transforming the integrand, find du. A 18e-2xdx B - 18e-...

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Q: The curve C with equation y = f(x) passes through the point (1, -3). Given the following, find f(x) ...

A: We know, ∫xndx= x(n+1)/(n+1)

Q: Determine whether the series converges. k=1

A: We use limit test to find convergence or divergence of given series. Follow 2nd step.

Q: From the roots of indicial equations, identify the general form of the first and the second solution...

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Q: 12) cos? 0 = 1 %3D

A: For given trigonometric function we have to find out values of ( x  ) such that                    C...

Q: sin 3x Given: -dx_what is the appropriate formula to find the integral?- cos2(3x) (4-3 sec 3x) A du ...

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