The radius of a sphere is increased from 20 cm to 20.2 cm. Estimate the change in volume.

Q: Find the area of the region under the graph of f on [a, b]. f(x) = x2 - 8x + 20; [-1, 2]

A: The detailed solution is given below Thank you

Q: Determine whether the integral is improper (x-4) -'dx A Improper B Not improper

A: Given data÷

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the…

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Q: dF Find given F(x) = (3s - 4) ds. %3D dx dF dx %3D

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Q: Evaluate the integral. 3 if -2 < x< 0 f(x) dx where f(x) | 4 – x² if 0 <x< 3

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Q: A ball is shot from the ground straight up into the air with initial velocity of 49 ft/sec. Assuming…

A: Let's find.

Q: at x = 2 for the function below. dx Evaluate y = - 5u? + 4u + 9, where u = 9x2 – 2x + 4 Answer…

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Q: Let C1 be the curve with parametric equations x = cos t, y = sin t – t, where t E [0, 5]. (a) Find…

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Q: Use De Moivre's theorem to solve for z given z = 3 – 2i. Write your answers in rectangular form. Use…

A: Given: z5 = 3-2iz   = 3-2i15                                     1-------------------De-Moivre's…

Q: Calculate the higher derivative. (Use symbolic notation and fractions where needed.) d? 8 cos (1) =…

A: To find,  d2 dt28 cos2(t)

Q: t $14.15, the demand (customers) for UB-shirts is 400. When the price increases to $15.25 the demand…

A: Given query is to find the demand at given point.

Q: Find the area of the blue region. It is the area under the curve. 8 y = 3 x + 1 4 y =7– x 2 4 6 8.

A: This question can be solved using the concept of area under curve.

Q: ¤(x+4)~²dx

A: Here we have to find the given indefinite integrals.

Q: 4- Find lim,: ( -) 10 20 (You cannot use numerical table method). tan(2)-1 tan?(2)–1)

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Q: 1 Find Vf if f = 2 /x²+y² +z?

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Q: d²y Find the second derivative, dx2 a. x = t² + 1 and y = t³ t2 b. x = 2 · + 2 and y = sin(t + 1)

A: This question can be solved using the concept of second order derivative.

Q: 12. L(s? – 1) sds 13. (1² – #) dt

A: ∫xndx=xn+1n+1+C , C is a constant for any real number n.

Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 3…

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Q: 4. Find the exact value of the expression. (a) 10log 36 (b) In e3

A: Explanation of the answer is as follows

Q: Find the arc length L of the graph of r(t). 1 r(1) = r} i + t j+ Vor² 2<t< 5 L =

A: We need to find arc length.

Q: Verify Green's Theorem by evaluating both integrals aN y? dx + x² dy = /, J da ay ax for the given…

A: We have to verify the green theorem for the

Q: Find the particular solution of the following ODE given that y(0 d’y +y=e* dx

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Q: 16. Interpretations of Integrals Determine the position function, s(t), of an object if the…

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Q: What is the length of a laptop computer centimeters or meters

A: We have to tell the unit of length of the laptop.

Q: 10 9. Consider the function f(x) %3D Let F(r) be the antiderivative of f(z) with F(1) - 0. Then F(x)

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Q: Find the consumers' surplus at a price level of p= $160 for the price-demand equation below. p =…

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Q: 2 2 of

A: Please see the answer below.

Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

A: Find Maclaurin series.

Q: 2. Given f(x) = x' + ax² + bx has critical numbers at x=1 and x=3, find a and b. .2

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Q: Let C1 be the curve with parametric equations x = Cos t, y = sin t – t, where t e [0, ). (a) Find…

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Q: Evaluate the definite integral. e141 i + ej +t k )dt O e14 – 1 1 Li+ (e- - 1) j+, k 14 (e4 – 1) i-…

A: Definite integral

Q: Write an equation for the function graphed below. Use the smallest powers possible to meet the…

A: To find the equation of given graph.

Q: The acceleration function (in m/s²) and the initial velocity v(0) are given for a particle moving…

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Q: Question 6 dx Evaluate the integral improper integral (2r – 1)3 A 1/9

A: Given: ∫-∞ 012x-13dx

Q: Question 3 Find the area enclosed by the curves y y = 2 V1- 9x2 O V5- 9. 2n B 3 5n D 6

A: Solution is given below:

Q: 2 sin (csc 2x) dx

A:

Q: 9. Find the sum. (a) 22 32 23 33 29 34 310 (b) 1 + 2/2 23/2 11 1/2 1.

A: b)1+1212+12+1232+.........

Q: Find the arc length L of the graph of r(t). r(t) = 4 cos(t)i + 4 sin(t)j+ tk, 0<t< 2m L

A:

Q: Consider the function f(x) = -4xi + V24 -x on the interval [7, 27]. Find the absolute extrema for…

A: We want to find absolute maximum and minimum.

Q: Evaluate the definite integral. e141 i + e-j +t k )dt O e 4 – 1 i + (e-1 – 1) j +, k - 14 (e4 – 1) i…

A:

Q: 4. Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: We have to calculate indefinite integral ∫{(3x2+6) /(x3+6x) }dx Let us say  I = ∫ {(3x2+6) /(x3+6x)}…

Q: a. Suppose that Miller Corporation can produce 3500 refrigerators when the number of hours of…

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Q: 1. メーメー2 xペー5x+6

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Q: For the following conditions, where "x= number of roses" and "y= number of daisies", determine…

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Q: Calculate the first five derivatives of f(x) = – sin(x). Then determine f(8) and f(9). (Use symbolic…

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Q: | (2x - y) dx + (x + 9y) dy. Ic Evaluate C: x-axis from (0, 0) to (0, -9) and (0, -9) to (5, -9)

A: We can solve as follows

Q: 4 dx 16 + x² 2 dx X/x² – 4 2

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Q: Use Newton's method to approximate a root of the equation x + x + 4 = 0 as follows. Let 1 = - 1 be…

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Q: ||r'(t) x r"(t)|| ||r(t)||° Use the formula k(t) = to find k(t). 13 r(t) = t°i+ t°j K(t) =

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Q: Let f be a function defined for t 2 0. Then the integral L{f(t)} = e-stf(t) dt is said to be the…

A: Given problem:-