Find the volume of the solid formed by rotating the region enclosed by y = e²x + 5, y = 2x + 5, y = 0, x = 0, x = 0.7 about the x-axis.

Q: For the following demand function, find (a) E, and (b) values of q (if any) at which total revenue…

A: For the following demand function, to find  (a) E, and (b) values of q (if any) at which total…

Q: Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate this…

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Q: dy Find by implicit differentiation. dx x²14xy + y² = 14

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Q: Determine if the series O O A n = 1 ² n2 +4 5 n2 + converges or diverges and choose the option that…

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Q: A volume is described as follows: 1. the base is the region bounded by y = 7 64 2. every cross…

A: The base is the region bounded by y=7−764x2 and y=0. And every cross section parallel to the x-axis…

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Q: Let f be the function defined as follows. y = f(x) = √√√√5x + 6 (a) Find the differential of f. dy =…

A: A detailed solution is given below.

Q: Use logarithmic differentiation to find the derivative of the function. y'(x) = X-3 x + 3

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Q: Q12 Construct the equation of the line passing through (0, -2) and (3,5).

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Q: Find the arc length of the curve y = ln x - ² on the interval [1, 3].

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Q: 9. 87 12 5 -

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Q: You are planning to make an open rectangular box from a 38-in.-by-75-in. piece of cardboard by…

A: This question is based on application of derivative. First take a square of length x then make a box…

Q: Consider the center of mass of the following. A lamina occupies the part of the disk x² + y² ≤ 9 in…

A: The solution is shown below- As per company guidelines only first three parts are allowed to solve.…

Q: We need to minimize the cost (measured in units of $100,000) of the pipeline, C(x) = 20✔ 20 5 x +…

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Q: Find the derivative of the function. -7x³ - 6 6x² +7 f(x)=

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Q: Determine the derivative of each function f(x) = 3x³ + 2x² [K2] 1 b. f(x) = = = − 2x² [x2] x² c.…

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Q: Find the relative maxima and relative minima, if any, of the function. (If an answer does not exist,…

A: We find the first and second derivatives using the power rule F(t)=3t5-20t3+20F'(t)=ddt3t5-20t3+20…

Q: Suppose that the position of a particle is given by f(t) = 5t³ +7t + 9. s = f(t)

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Q: The Ninth Gate You arrive at the final gate, which leads into a building-like structure. You hope…

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Q: 6 Function f is defined by [1-e, x0

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Q: Question 17 () Let / be defined as follows: {² z Using the definition of the derivative, compute…

A: Let f be defined as follows:  fx=x2 if x<0x if x≥0 By using the definition of derivative, to…

Q: [√² √sec²z - 1

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Q: Let f(x) = x² 50x² – 8. Calculate the derivative f'(x) = Calculate the second derivative f"(x) =…

A: Please see the below picture for detailed solution.

Q: The tangent to (2,4) on the graph of a function f(x) is y = 5x - 6. Evaluate f'(2). (a) 5 (b) 4 (c)…

A: We have given the equation of tangent line y=5x-6 of f(x) at point (2,4).

Q: Every year, Danielle Santos sells 59,200 cases of her Delicious Cookie Mix. It costs her $2 per year…

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Q: (x+1 Q. #7 For the function g(x) = 3 if x 2 constant "b" that makes g(x) continuous at x=2 Final…

A: g(x) is continuous    here we find value of b by using condition of continuous function

Q: 4sqrt(2) was incorrect

A: Given:= f(x,y) = x3y2U = (-3,3) P= (-1,-2)   The directional derivative being negative means that…

Q: Find the limit lim x (tan x) cos(x)

A: L'Hospitals Rule:

Q: 4.4. Solve the equation ff(x) dx = sin x - 2 tan x + 7x HELP: Treat ff(x) dx as a variable and use…

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Q: The Fourth Gate You arrive at the fourth gate, feeling confident in your skills. "It is a good thing…

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Q: Estimating the Amount of Paint Required A coat of paint of thickness 0.07 cm is to be applied…

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Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

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Q: Find the critical point of the function f(x, y) = 4+ 3x + 2x² − 4y − 2y² This critical point is a:…

A: Need to find out the critical point of the given function.

Q: 14. The domain of the function is y 4 2 -4-20 2 4 x

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Q: You are designing a rectangular poster to contain 32 in² of printing with a 2-in margin at the top…

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Q: 1. a. Consider the following graph of a continuous function f(t) on 0 ≤ t ≤ 10. 2 s(t) p/ 0 6 10 4…

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Q: Find lim f(x) if, for all x > 1, x → 00 4 12ex - 24 4ex X 3√x √x-1

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Q: Find the derivative of the function. In(e²x + 3) y =

A: y=lne2x+3d dx(lnx)=1xd dx(ex)=ex

Q: Suppose that f is differentiable at 1 and f'(1) = 1 = f(1). Evaluate x¹ f(x²+x-5) - 16 x²4 lim x-2

A: Given f is differentiable at 1 f'(1)=1=f(1) We are required to find limx→2x4fx2+x-5-16x2-4

Q: Write the equation of the tangent line to the curve at the given point. x² + y² + 6x - 3y + 7 = 0 at…

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Q: Find the derivate of the functions a) F(x) = (7x²-9) (2x + 7) f'(x) = b) f(x) = 8x² - 2 8x +3 f'(x)…

A: To find derivatives

Q: Let S = {1, 2, 3, 4, 5). Let f S S be the function defined by f = {(1, 1), (2, 1), (3, 3), (4, 3),…

A: Sol:- To count the number of functions g: S→ S that satisfy the given condition, we need to first…

Q: Find parametric equations of the line that contains the point P(3, 1,-2) and intersects the line L:…

A: The solution is shown below-

Q: 17x³ (In x)² dx =

A: The given integral is: ∫17x3 ln x2 dx

Q: 1 e) lim (-—-—-₂--²-4) x-3x-2

A: M=limx→3(1x-2-4x2-4)

Q: Consider the function f(x) = 1−3x², -3 ≤ x ≤ 1. Use the derivatives to algebraically answer the…

A: Given, As per given question we need to find the extreme points of the function fx=1-3x2 on the…

Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: Given differential equation:- x2+y28dy=7xdx+ydy

Q: -4 +00 24 y 2 -20 -2 4 2 4 ४ c. 1

A: we will find the required.

Q: Sketch a graph that possesses the characteristics listed below. f is increasing and concave up on…

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Q: 15 sin ¹√2x dx = [

A: