w = sqrt(25 - 4x2- 4y2),  x=r cos(theta),  y=r sin(theta) (a) Find del w / del r and del w / del ? using the appropriate Chain Rule.

Q: 20. The graph of the first derivative f' of a function f is continuous on (-∞, ∞). -2 -1 f'(x) 1 2 3…

A: According to Bartleby guidelines I can only answer the first three sub questions of the given…

Q: Use the graph below to answer the following questions. f(c) -6 -4 5 14- 12 10- 8 6- 4 2- 2 -4- -6-…

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Q: The graph of y = f(x) is shown. Use the graph to answer the question. Find lim x-(-1)- O-2, -7 O-7,…

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Q: Find each of the following for f(x) = 6x² - 6x +6. (A) f(x+h) (B) f(x+h)-f(x) (C) f(x+h)-f(x) h

A: In this question we have to find the following given parts in the question.

Q: 2. Find the trigonometric integral. (Use C for the constant of integration.) Star tan(0) sec³(0) de

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Q: Prove, using integration, that the volume of a sphere with diameter "d" is πYd³ 6

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Q: Question 3 [ For the system of linear equations -3x + 5y = 4 ny + 12x = -16 a) [: Find the values of…

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Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y = 11e2x, y(0) = 1, y'(0) = 1 2x -7.x 7e…

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Q: Suppose u v = T. . Which of the following is a possible angle between u and v? O 90° O 120° O 35° O…

A: Here, given that u, v∈ℝ3 and u·v=π

Q: Given the function of two variables f(x, y)= ln (√x + y6) The partial derivative with respect to x…

A: using the partial derivative,

Q: Evaluate the definite integral. 3 1₁(x-41 4|x) dx

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Q: Use the half-angle identities to evaluate exactly. sin 112.5° sin 112.5° = (Simplify your answer.…

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Q: Question 2 i 1: a)' Solve the following linear system in detailed, by using Gauss-Jordan…

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Q: 2. Approximate 64.1 by using linearization and use a calculator to compute the percentage error.

A: Given :64.13

Q: For f(x) = (x + 1)²-3 where x > -1, find: a. The inverse function, f-¹(x) b. The domain of f-¹(x) c.…

A: Given f(x)=(x+1)2-3 We know that, A function g is the inverse of function f if for y=fx,…

Q: 1.) Sand hole conical pile altitude always 1 4 of increasing when the 14 pouring from a the conical…

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Q: Let h(x)=f(x)g(x) where f(x)=−3x2+4x−1 and g(x)=−x2+4x+3. What is h′(4)? Do not include "h′(4)=" in…

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Q: e −1 -1 lim (−1) t⇒0 t

A: Use limit expansion

Q: If z = -4xe³xy and x = √t, y = . Then, the value of dat t = 8 is equal to 3√2 (-1/2² + 2³/1) e + ² 4

A: This question can be solved using the concept of derivatives.

Q: b. Stan ³0 sec²0 do

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Q: Determine where the function m(x) = x + 1 (x-1)(x-7) is continuous. The function is continuous on…

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Q: In a classic video game, balloons travel from left to right along a linear path that passes through…

A: Given equation is :   x-12+y2= 100 ---- equation of circley=3x+7 --------equation of line

Q: 3. Evaluate the definite integral below: S¯¼ √x² + 2x − 5dx + Sq − √x² + 2x − 5dx

A: To solve the following integral problem

Q: Find all the values of x such that the given series would converge. (x-8)" 8n n=1 The series is…

A: We will use ratio test.

Q: Sketch the region enclosed by the curves and find its area. Enter the exact answer. Area = y = 2x²y…

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Q: The area of an ellipse with axes of length 2a and 2b is given by A = Tab. Approximate the percent…

A: Concept: We have given the Area A=πab Here the length a is increasing by 2% which is daa=2% Here the…

Q: 16. M8 Σ n=1 –3η + 1 2n + 3 4η

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Q: find the unit vector in the direction of u u=

A: find the unit vector in the direction of u u=<-4,-1,-3>

Q: given u= and v= find uXv

A: To solve the following problem

Q: Solve, finding all solutions in [0,2x). 4cos x + 4sinx=2√√6

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Q: Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the marginal…

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Q: Question 5 Test the series below for convergence using the Root Test. 5)₁ ∞ n=1 f(n): 3n 6n + 5 The…

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Q: Multiply and simplify. (1 + tan ß)² (1 | + tan ß)² = [ (Simplify your answer.)

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Q: Find the average value gave of the function g on the given interval. 9 ave 11 g(t) = t √8+2² 8 + t…

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Q: 3. What are the values of A, B, and C so that a. A = -2, B = 3, and C = 4 b. A = 2, B = 3, and C= -4…

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Q: Find the exact value of the expression in radians and degrees. -¹(2) -1 sin Find the exact value of…

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Q: c) x² + xy = 2x² +1. d) = 2² sin(3r) +2. d

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Q: (d) Determine the y-intercept(s). (e) Sketch the function. (f) Determine the axis of symmetry. (g)…

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Q: (a) Give the linearization L(x) of f(x) at x = 2. (b) Use your answer from Part (a) to estimate the…

A: Solve the following

Q: Rewrite the following equation with the variables separated. 3√t + y² dy = 6 dt o y² dy = (6 + 3√t)…

A: Please see the below picture for detailed solution.

Q: S." (inx+4)" x dx

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Q: The region is bounded by the curves of y = x² and x = y². Find the integral in line y = -1. Use…

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Q: If f′(−6)=7, and g(x)=−3f(x), what is g′(−6)? Do not include "g′(−6)=" in your answer. For example,…

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Q: Given that S." sin xdx = 2, find the average value of the sine function on the interval [0, π].…

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Q: Find the radius of convergence, R, of the series. R = 00 Σ n = 1 7 || xn 4n - 1 Find the interval,…

A: We have to find out the interval

Q: Determine whether the improper integral diverges or converges. 16 1 √√√x dx converges diverges…

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Q: L) Prove that (3-2)(x+2) = 3 +21 iFitwas

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Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y= 11e²x, y(0) = 1, y'(0) = 1 2x 7e -7.x…

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Q: Let S be the plane with equation 2x - 3y + 4z = 1. Find parametric equations of a line that goes…

A: Explanation of the answer is as follows

Q: find the area of the triangel with verticies A=(0,0,0) B=(2,1,1) C=(3,1,2) round to 2…

A: This question can be solved using the concept of area of triangle using vectors.