Question 12 If A is the area of a variable square with side s, what is the rate of change of A with respect to s at the instant when the side of the square is 4 c O4 square cm per cm O 8 square cm per second O 8 cm per second O 8 square cm per cm

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A: Explained below

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A: See the answer below

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A: This question is related to series and sequence, we will solve it using given information.

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A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

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Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper…

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Q: 7 Given the graph to the right, find 0 7 0 f(x)dx = f(x)dx Ау 10- 8- 6- 4- 2- 0 2 14 Foo 6 co. 8 X…

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A: This question is based on area and integration.

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Q: C 5 4 3 2 1 1 1 2 3 4 5 To find the blue shaded area above, we would calculate: J. f(x) dx = area…

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A: For second order differential equations that cannot be solved be algebraic methods, the leibniz -…

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Q: Problem 5. An observer is positioned 3km away from a rocket launch pad. How fast is the distance…

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

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Q: (1) 5. How many different class pictures can be taken if there are 2 teachers and 15 students and…

A: This is a problem related to permutation and combination. Based on the general formula and concept…

Q: 9) xdy- ydx = (x² + y ² ) ex dx a) artan. * =* b) arctan X = ţ c) auctan $ d) none of the above etc…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: Given f(x, y) = 6x6 – 6x²y³ – 5y³, find fz(x, y) = fy(x, y) = fiz(x, y) = fry (x, y) =

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Q: Evaluate toivancos You G₁ (nty) dv kab

A: To evaluate:  ∫∫∫Gx2+ydvWhere G is the solid bounded by z=y2 and in xy plane x=0 to x=4 and y=-3 to…

Q: Eliminate the arbitrary constants of the following. Simplify your answers.  4. y = c1x^2 + c2x^3

A: Given problem:- Eliminate the arbitrary constants of the following. Simplify your answers.    4. y =…

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Q: If F(x) = f(g(x)), where f(−2) = 4, f ′(−2) = 3, f ′(5) = 5, g(5) = −2, and g ′(5) = 4, find F…

A: NOTE: Refresh your page if you can't see any equations. . here we have f(−2) = 4, f ′(−2) = 3, f…

Q: Determine the critical numbers for f(x) = (x-a)*(x-b)*. Ox=a, x=b and x=m+n h Ox=-a, x=-b and x=n+m…

A: Since you have asked to solve two sub questions we will solve it.

Q: Problem 1: At what points is the function y = form. 2x²+10x+12 x²-5x continuous? Write your answer…

A: In this question, we want to know the points (in the form of interval) at which the given function…

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A: I have appended the formula used in the solution part of the question

Q: Choose the letter of the correct answe. 1) x² (xdy + ydx) = (5- xy) dx a) x ln (5-xy) = 1- cx b) -x…

A: We are allow to solve first question only .If you need rest of answer please upload it separately…

Q: Problem 3: The graph of h in the figure below has vertical asymptotes at x = -2 and x =3. Find the…

A: Topic = Limits

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Q: Find an expression in a and b for the value of the definite integral: [9x² + √x-8]dx. A. 3 (b³a³) +…

A: The objective of the question is evaluate the definite integral.

Q: Tutorial on 1. Find Let cos²t } -St f(t) dt dt 11 e - St Laplace Transforms Also D to fe S tcost

A: Concept: Using the formulas: L{tnf(t)}=(-1)ndnF(s)dsn................(where…

Q: Indeterminate Form 4 7. lim 2 1–cosx x-0 4 1 8. lim x-2x²-4 x-2 9. limsin 3xcot 2x 10. limx²e 11.…

A: We have to determine the indeterminate forms.

Q: Find the absolute maximum and minimum values of f(x,y)= x²-2xy+2y on the rectangle defined I by x in…

A: We need to find absolute maximum and absolute minimum on guven region.

Q: Solve for y at x=2: (4x^3 - 6yx^2 + 2xy^2)dx + (2yx^2 - 2x^3)dy = 0; y(1)=4

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Q: Which of the following series is converges or diverges. If the series converges, find its sum? 2+2

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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Q: Refer to the graph of y = f(x) = x² + x shown. a) Find the slope of the secant line joining (-4,…

A: Given:    f(x) = x2 + x

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Q: Approximate the area under the curve over the specified interval by using the indicated number of…

A: f(x) = 25 − x2 from x = 1 to x = 5; n=4 subintervals

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A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Evaluate the integral. [ f(x) dx where f(x) = 4 2 5-x² if -4 ≤ x ≤ 0 if 0 < x≤ 2

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Q: If y = (3 + 2x), what is y"? 00 48(3 + 2)2 © 12(3+2r)? O24(3 + 2)²

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Q: • Example: f(x, y, z) = x³ + 3xy + 3xz+y³ + 3yz + z³ • Find the stationary points • Classify the…

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Q: -5e 1 Evaluate the integral: dx. 1 x A. - - 1 5e B. 1+ In 5 C. 0 D.00

A: We have to evaluate to integrate

Q: 4) Find the point in which the line through the origin perpendicular to the plan 2x - y -z = 4 meets…

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Q: Find the directional derivative of the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

Q: Sales of a particular product have been declining continuously at the rate of 15% per year.  a.)…

A: Given ,  Sales of a particular product have been declining continuously at the rate of 15% per year…