Consider the function f(x) = 12x², − 4 ≤ x ≤ 1. The absolute maximum value is and this occurs at x = The absolute minimum value is

Q: Assume that the radius r of a sphere is expanding at a rate of 7 in/min. The volume of a sphere is V…

A: Differentiate volume wrt t then put value

Q: Evaluate the integral 32 3 √2³ (2² (x² − 2) dx =x²-2. by making the substitution u = x² + C

A: We know, ∫xndx= xn+1/(n+1) +C, C is a constant and for any real number n. Let I=∫x³(x⁴-2)³²dx

Q: Write an equation describing the relationship of the given variables. y varies inversely as the cube…

A: Given that y varies inversely as the cube root of x.

Q: Use the Ratio Test to determine whether the series is convergent or divergent. Identify an n = 1…

A:

Q: Suppose that f(x, y) = 2x + 7y and the region D is given by {(x, y) | − 5 ≤ x ≤ 3, -5 ≤ y ≤ 3}. D…

A: To find the double integral value.

Q: - Evaluate: f Sin (x7 - 5) dx x

A: ∫sinxdx=-cosx+cdxndx=nxn-1

Q: 3 If f(x) = (5x + 5)-³, find f'(x). f'(x) = Find f'(1). Enter the exact value as an expression.…

A:

Q: Find the number or limit approached by the entire function as h approaches 0: 3h² a. lim h→0 h Find…

A:

Q: Activity 3.4.2. A soup can in the shape of a right circular cylinder is to be made from two…

A: To determine the objective function

Q: 2. Find the tangent line at the given point c(t) = (4t, In (t)); t = 1

A:

Q: 4. A line segment L passing through the point (1, 1) has its endpoints lying on the x-axis and…

A:

Q: ܢ Find an antiderivative of Antiderivative = 9 z2+9 4 25 in the variable where > Remember to include…

A: To find the antiderivative function.

Q: Find the value of X 56 35 イメー

A: Given query is to find the value of x.

Q: The graph below is the function f(x) 5 4

A: From Graph : f(2) = 1limx→2f(x)=2≠f(2) Therefore limit does not existThe function is not continuous…

Q: 2- Find the equation of the tangent line to the curve 9xCos(7y) + 5y = 9 at y = 0.

A: To find the equation of the tangent line to the curve 9x cos7y+5y=9 at y=0.

Q: . For the given triangle, find the exact value of all six trigonometric functions. Function sin 0…

A:

Q: 26) Suppose that f and g are continuous and that Ś [4f(x)+ g(x)] dx. Find f(x) dx = -2 and ľ g(x) dx…

A:

Q: The value of 5 1 x² [³ - dx is

A: Given query is to find the value of integral.

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. [Hint:…

A:

Q: A forest fire is found at midnight. It covers 1200 acres then. It is spreading at a rate of f(t) =…

A:

Q: Give the equation of the tangent line to the graph of the function y = x - ln(2x) when = Give your…

A:

Q: g(x) = x 24 353 3x find and simplify g(x)-g (a) X+5 Given that g(x)= x-a

A: Solve the following

Q: Which of the limits is equivalent to the following definite integral? Se e² dr Choose 1 answer: B…

A: To determine the limits which is equivalent to the following definite integral.∫03ex dx

Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and f'(0) = 3,…

A: Given: f(0)=1, f’(0)=3 and g(x) is the inverse of f(x) To find: g’(1)

Q: If f/u) = sinu; then (fog)'(3) = ? B) 1 = g(x) c) 6 10 kone E) None D) 9 A hind S'hospitals

A: f(u)= sin u u=g(x)=x2-9 To find (fog)'(3)

Q: . Let ƒ(x) = (x² - 4)³. Do the following. (a) Find the maximum value and the minimum value of f on…

A: We have to solve given Questions.

Q: The Maclaurin series for cosx is ...? O a) 1 + +2 +4 +6 2! 4! 6! ○ b) x - - 6 + .... 21 + 21 − 2 +…

A: f(x)=cosx The Maclaurin series of a function is given by :…

Q: dy 13) y = (x+2xT; 2 =? A) X+L y D) B) 4y (Xi) (XH) (x + 2x-1) 3/2 c) 1 21Xষx

A:

Q: Find the parameteric equation for the line segment starting at P(-2,3) and ending at Q(-3,2)

A: Given that:- The line segment starting at P(-2,3) and ending at Q(-3,2)

Q: 8). Hy is a a differentiable function of X, then the slope of the curve of; 3 ³ = 6 at point where…

A:

Q: For question d, is it -5 over 4?

A: For question d, is it -5 over 4?

Q: 7x+2 8- Find S dx (Using substitution method). √7x-3

A:

Q: ate the integral. Prox f(x) dx where f(x) = 2 if -2 ≤ x ≤ 0 {²₁ - x² 14-x² if 0<x≤2

A: Given is to find the integral

Q: Find all the antiderivatives of the function f(x) = -6.

A: ∫xndx=xn+1n+1+cgiven  f(x)=-6

Q: a 10) a 26 foot lodder bons against building so that it foot moves away from the building at the…

A:

Q: Calculate the iterated integral. 1 / 1 ["'f's Jo Jo 5 √s + t ds dt

A: Given,           ∫01∫015s+tdsdtTo find : Calculate the iterated integral

Q: Compute • d da - [In(1+x)²].

A: NOTE: Refresh your page if you can't see any equations. . use the log rule

Q: Give the equation of the tangent line to the graph of the function y = ln(e+z) at x = 0. Give your…

A: equation is   y=mx+cwhere m is slope and m=dydxd dx(lnx)=1xwe know that  lne=1

Q: 2 (b) ₁² ( + 6x) dx X

A: ∫xndx=xn+1n+1+c∫14(2x+6x)dx=2∫141xdx+6∫14xdx

Q: f(sin (6x))³ dx

A: According to our guidelines, we can answer only one question or the first three subparts of a…

Q: Express the solution to the following inequality in interval notation. 6 2x + 1 ≤2

A:

Q: Given the points P(−2, 3) and Q(−2, −5), find the magnitude and direction of PQ. Provide your answer…

A:

Q: Use properties of the indefinite integral to express the following integral in terms of the simplest…

A:

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Figure

Q: Suppose f(x, y) = 5y - 9x Find an equation for the level curve of f that passes through the point…

A:

Q: dy dr || (b) Find dy dx || (a) Find as a function of t for the given parametric equations. dr dy as…

A:

Q: A curve is given parametrically by=et 2e-t, y = e2t. The tangent t the curve at t = ln 2 is...? a)…

A: Given x = et - 2e-ty = e2tat t = ln2

Q: Suppose you are driving away from Morgantown. At noon, you are 75 miles away from Morgantown. From…

A:

Q: Calculate the iterated integral. 13 3 2 LI (6x2y – 5x) dy dx /1

A: To evaluate the given double integral

Q: Use a triple integral to find the volume of the solid bounded by the graphs of the equations. z = 6…

A: Given that some equation z= 6-x3 and y= -x2+2 And y=0 ; z=0 ; x&gt;=0 . Use triple integration to…