Find two other pair of polar coordinates one with r>0 and r<0 for  (6,π/4) (-5,3π/2) (3,-π/3)

Q: Find the derivative of the function. y = (tan-¹(7x))² y' =

A: y=(tan−1⁡(7x))2Take derivative.y′=ddx((tan−1⁡(7x))2)Use the derivative rule:…

Q: Use Cramer's Rule and the four-step method given in the lecture notes to solve the given system of…

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Q: Find equation of the tangent to the curve at the given point x=t^2-4t, y=t^2+4t+1; (0,33)

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Q: 1. Power Rule: d dx Special Case of this: (x²) = nx" 4. Quotient Rule: n-1 U ( ² )' = d dx 2.…

A: C(x)= (5 x-2 )( 3 x2+ 4 x)We have to find marginal cost and for this we have to differentiate C(x)…

Q: y=xsin'' x+√√₁

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Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: In the question we have to find the number of units which will provide maximum profit.

Q: Practice 1: Use the limit lim 8-0 sin =1 lim tan 41 1-0 sin 31 and trig identities to evaluate the…

A: Limt-0 tan(4t)/sin(3t)

Q: H.W// solve the following equation: 1. y"-4y' +7y=0.

A: y" - 4y' +7y =0auxiliary equation is given by m2-4m+7=0.

Q: Question 3 (a) Find and sketch the domain of the function f(x,y)=√x-1+√y-4 (b) Evaluate the limit…

A: Domain: Domain of a function f(x,y) is the set of values of ordered pair (x,y) such that f(x,y) is…

Q: (c) Part of the graph of g(x) = x + x² is given below. Use calculus and algebra to find all possible…

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Q: Improper Integrals, Infinite Limits of Integration: Integrals may have infinite limits of…

A: The given integral converges.

Q: (b) y = arccot (cos)

A: The given functions (b) (c)

Q: Two poles are connected by a wire that is also connected to the ground. The first pole is 50 ft tall…

A: Given:To Find:

Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. lim (15x +…

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Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

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Q: Find a graph up and down from the equation g (x) = (x + 1) (x-2 )

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Q: Use the Integral Test to determine whether the series shown below converges or diverges. Be sure to…

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Q: Use the transformation x = au and y = bu to find the area of an ellipse with equation + = 1. (Hint:…

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Q: What is called a quadratic equation and give 3 examples by calculating its factors with detailed…

A: I have appended the formula used in the solution procedure

Q: Extrema on a sphere Find the points on the sphere x² + y² + z² = 25 where f(x, y, z) = x + 2y + 3z…

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Q: a. Find the critical points of the following function on the given interval. b. Use a graphing…

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Q: Factor the following problem and show your complete solutions D32D²5D +6

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Q: The line segment x = 1 - y, 0 ≤ y ≤ 1, is revolved about the y-axis to generate the cone in Figure…

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Q: Find the length of the curve 3= + e), Setup the integral. dy 2 ° ² - [ √ - - - _ ) « - / √ - + [ } @…

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Q: Evaluate the limit. lim X→-00 49x² - 1 x + 7

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Q: A semicircle of radius r = 5x is inscribed in a rectangle so that the diameter of the semicircle is…

A: Consider the figure

Q: Use the root test to determine if the following series converges or diverges. 80 Σ n=1 5 (4 +…

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Q: Let f(x) = 3x³9x² - 27x + 23. Find f'(x) and all values of x for which f'(x) = 0. Explain the…

A: we need to find out the first derivative and also solve for f'(x)=0

Q: Integrate the following: [√²+eda 1+ e dx

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Q: Using linearization, show that sin(x) ≈ when ≈ 0. Apply that to approximate sin(√0.0001).

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Q: 00 Consider the series Σ (19x)" n=0 (a) Find the series' radius and interval of convergence. (b) For…

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Q: Find the volume of the solid generated by revolving the region bounded by, y=3√√x and x=8 about the…

A: we need to find out the volume of the solid generated by revolving the region that is bounded by the…

Q: Knowing that cos(22.5 deg) = (1/2)(square root of 2 + (square root of 2)), find the exact value of…

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Q: Solve 11 (ex) ¹¹e13 + 6x = 4 5In (3) 17 5 In(3) +- In(3)- 19 11 243 13 17 13 6 +5 In(3)

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Q: 4. Let R be the parallelogram enclosed by the lines x + 3y = 0, x + 3y = 2, x + y = 1 and x + y = 4.…

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Q: The region bounded by the curve y = √x, the x-axis, and the line x = 4 is revolved about the x-axis…

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Q: Given f(x) = (5x²-x) ¹ ƒ'(x) = You do noted to simplify

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Q: Given √√² + 4y = x, find Answer Attempt 3 out of 4 dx in terms of x and y.

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Q: Evaluate the iterated integral 1 1 -3 0 18x5y²dy dx.

A: I=∫−31∫0118x5y2dydx

Q: 3 2 10 -7 -6 -5 -4 -3 -2 -1 TO -2 -3 -4+ X given below to 2 3 4 5 6

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Q: Find the largest product the positive numbers x, y, and z can have if x+y+z² = 16.

A: x+y+z2=16Find the largest product of the positive numbers x, y and z.

Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A: To find the critical points of the following function. By using the Second DerivativeTest to…

Q: Find equation of the tangent to the curve at the given point x=sin(πt), y=t^2+t; (0,30)

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Q: Find the absolute maximum and minimum values for the given function over the specified domain. f(x)…

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Q: Solve the inequality. Write the solution set in interval (+5)(y-1)(y-6) ≥0

A: (y+5)(y−1)(y−6)≥0

Q: A) Find the derivative of f(g(x)) at x=2  if f(2)=6, g(2)=3, f'(2)=1 and g'(2)= -2

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Q: Let f (x) 8-x-x² if x ≤3 2x-7 if x>3 Calculate the following limits. Enter "DNE" if the limit does…

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Q: Find the exact average value of f(x) = rlnr on the interval [1, e] (do not approximate).

A: The average value of function f(x) over the interval  is The given function is

Q: y = sin-¹(6x + 1)

A: y=sin−1⁡(6x+1)

Q: Find the absolute extrema of the function over the region R. (In each case, R contains the…

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