256x The volume of a sphere is increasing at a rate of 8 cm³/sec. Find the rate of change of its surface area when its volume is 3 OA. cm²/sec 8 3 OB. 16x cm²/sec 64 3 ⒸD. 4 cm²/sec O C. cm²/sec cm³

Q: 5. Find the gradient of the line tangent to the following functions at the given points. a. f(x) =…

A:

Q: Let A(x) = √² ƒ 4 3 T -2 el -4 -5 * f(t) dt, with f(z) shown in the graph below. 3 At what a…

A:

Q: 6. Find the equation of the line tangent to the following functions ate the given points. a. y = x²…

A:

Q: 3 x¹ +1 dx

A: The given integral is (x4+1)/x2, limit from 1 to 3.

Q: I For f(x) = x-2 4x+20 (a) f(-6) (6) f(2) (C) f(-5) (a) f(a+3) find

A: The given function is To find:-

Q: Write the integral required to find the area of the region pictured below that is bounde 2(y+2) 3…

A:

Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

A: The objective of this question is to find the critical numbers and the open intervals on which the…

Q: Find the integral. Use C for the constant of integration. | cv² (y² + 3)² dy

A:

Q: Let sin A = (-1/sqrt10) with A in QIII and tan B =(3/4) with B in QI. Answer Exactly. Find tan (A+B)…

A: Given,

Q: lim n→∞ (1 + 1/2 ) ² = 2n

A:

Q: . If an item has a new cost of C and an annual depreciation rate of r (as a decimal), its value, V,…

A:

Q: Find the value of (fog)' at the given value of x. Assume that f'(3)=8, g'(4) = -6, g(4)=3, and y =…

A: The chain rule of differentiation is given by

Q: Find the domain of f(x). f(x) = Interval 3x - 5 x² + 2x - 35 Answer Attempt 1 out of 2 2 Answer…

A:

Q: Convert the Cartesian coordinate (1,-2) to polar coordinates, 0 ≤ 0 0 r = Enter exact value. 0 =

A: Cartesian coordinate (1,-2)

Q: 2x 1) Calculate the derivative of h(x) = √√e²x +e-²x

A:

Q: lim       sin(π+h)- sinπ                                      h→0     —------------…

A: Note:-Since your part a incomplete ,please repost part a again(b)

Q: A 17 ft. ladder is leaning against a building. The foot of the ladder is currently 9 ft. from the…

A: We have to use the concept of derivatives

Q: Find the parametric equation of a line segment with endpoints (1,4) and (5,-2). Find the parametric…

A:

Q: 1 e e 5. If A-), then ¹-(3) = eª = 01 0 e

A:

Q: Determine a definite integral that represents the area of the region enclosed by r = 7 sin 0. •b…

A:

Q: Evaluate the indefinite integral. [(arcsin x)² √1-x² -dx

A: We have given indefinite integral-First let's define that-

Q: 19. If $100,000 is invested at 6% compounded monthly for 7 years, the compounded amount is given by…

A:

Q: Find an antiderivative F(x) with F'(x) = f(x) = 5e" and F(0) = 0.

A: F′(x)=f(x)=5ex and F(0)=0

Q: f(x)=x^[8/3]-4x^[2/3] determin the: a) roots b) Domain c) intervals for which the function is…

A: The given function is To find:-rootsdomian intervals for which the function is positive and negative…

Q: The polar coordinates of a point are given. Find the rectangular coordinates of this point. (4,л)

A:

Q: Determine the integral by making the appropriate substitution. √9(x-1) 9(9x-10)' 'dx

A: To determine the following integral by making the appropriate substitution.

Q: DRAW THE GRAPH OF A FUNCTION WHERE limr-a f(x) DOES NOT EXIST FOR SOME INTEGER a. EXPLAIN WHY THE…

A:

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A:

Q: Starting with an initial value of P(0) = 50, the population of a prairie dog community grows at a…

A: The growth rate of population of prairie dog community is P(0)=50

Q: To check for the result, you have to prove that + C] = 8⁹. + sec²0. d 1 10 de Evaluate the left side…

A:

Q: The input value x = a is in the domain of the function g'. Explain the meaning of g'(a). Write an…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: For the function f(x)=x^3 - 3x^2 - 9x A. Find the critical points of f(x) B. Where is the function…

A: As per the company's guidelines, we are supposed to answer the first three sub-parts for you, Kindly…

Q: for Integrals Find or approximate all points a which the given function equals its average value on…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Find the surface area generated by rotating the given curve about the y-axis. x = 6t², y = 4t³,…

A:

Q: 5 -5 O 10 X

A: Given that the graph of the circlewe have to find the equation of the circle

Q: Which of the following is the correct result of 07 15 02 O 15 2016 -I +C 5 H wj* 05 1 21 :+C +0 of […

A:

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

A: Given,a(t)=t+4v(0)= 70=<t=<10

Q: 1. Decide whether each of the following sentences is valid, satisfiable or unsatisfiable: a) Smoke…

A: Here given a different sentences.The objective is to check that the given sentences are valid,…

Q: Find the vertex, focus, and directrix of the parabola with the given equation. Graph the equation.…

A: The given equation of parabola is The vertex form of parabola with the vertex  is

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

A:

Q: Solve the rational inequality x²-9 x² - 49 -≤0.

A:

Q: What is the second derivative x³ - 5x² + x = 0? A. 3x² - 5x B. 10x-5 C. 3x + 10 D. 6x-10

A: The given equation is Let

Q: 1. Find the area between the two curves. Be sure to show the representative rectangle in the 1st…

A: Given functions are,y=f(x)= 8 cos x and y=g(x)= sec2x

Q: A small resort is situated on an island that lies exactly 6 miles from P, the nearest point to the…

A:

Q: Vs = ft - f- f+ + f =

A:

Q: The equation of a hyperbola is (y + 3)2 - 16(x-3)² = 16. a) Find the center, vertices, transverse…

A:

Q: Functions f and g are given as follows. X 5 X+2 x + 2 Find each of the following functions and state…

A:

Q: Convert the Cartesian coordinate (-2,-5) to polar coordinates, 0 ≤ 0 < 2π r = Enter exact value. 0 =

A:

Q: Four Calculus II students have solved I sin sin(x) cos(x) dx. Their solutions are below. Use what…

A:

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

A: