Given F(x) below, find F'(x). Provide your answer below: F'(x) = F(x)= 2 cos (x) (1²-2) dt

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A: Marginal profit is the profit earned by a firm or individual when one additional or marginal unit is…

Q: Evaluate S2² (2x + 3e* − ¹) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23 e. NONE OF THE ABOVE

A: Given :∫122x+3ex-4xdx

Q: Evaluate the indefinite integral given below using the indicated substitution. /-20 -2(-2x +9)³ dx u…

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Q: If F(x) = = [₂√₂ x² a. F'(1) b. F(2), by interpreting F(2) as an area √4t - t² dt, evaluate the…

A: Given: F(x)=∫x20 4t−t2dt To find : F'(1) and F(2)

Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: We have to find the production for minimum average cost.

Q: IV. Solve the following problems completely. 3 1. Use local linear approximation to estimate √√(3.…

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Q: You are given the polar curve r = cos(0) + sin(0). (a) List all of the points (r, 0) where the…

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Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: Evaluate the following indefinite integrals. Show your solution. 1. f5 einx(sin x + cos x) dx ecos…

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Q: II. Evaluate the following integrals 3. S 3* sech³ (3¹) -dx 1+tanh (35)

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Q: Evaluate the following integrals. Show the solution.

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Q: Evaluate the indefinite integral given below using the indicated substitution. 1-20 -2(-2x + 9)³ dx…

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Q: Does the following graph represent a function that satisfies the following conditions? f(0) = -2…

A: Here we need to cross check the given conditions are applicable to the graph of the function or not.…

Q: Draw a direction field for the differential equation y'= (y - 9)². Based on the direction field,…

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Q: NUMBER 3 CLEAR AND SIMPLE

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Q: 3. Find the area of the region bounded by y=x²-2x +2 and y=6-x².

A: Use area under curve

Q: Determine the instantaneous rate of change of the function πt ³ √x sin 2 f(x) = LV x3 1 + √t at x=2.…

A: Leibnitz integral rule.

Q: a. Arc length of the curve y = 4- (x-2)² 4 bordering the region R

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Q: Daniel saved $260 at the end of every month for 4 years in his bank account that earned 5.60%…

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Q: Find the volume generated if the area between y = coshx and x- axis from x = 0 to x = 1 is resolved…

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Q: The graph below shows the direction field for y' = 6+3 y, and the initial point (to, yo) is shown in…

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Q: Find the volume of the sould generated by revolving the area bounded by the _given curves about the…

A: Let's find volume of solid (V) = ?

Q: The choice of u and du is subject to trial and error. Identify the appropriate choice of u and du…

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Q: dentify the surfaces of the following equations by converting them into equations in the Cartesian…

A: The given data is: To identify the surfaces: z2=4+4r2

Q: Use local linear approximation to estimate In (√0.99)

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Q: Perform the integration. (sinh x)(coth→ x + csch3x) dx

A: A detailed solution is given below.

Q: Define R as the region bounded by the functions f(x) = 3 and g(x) = x + 1 between x = 0 and x = 1.…

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Q: Determine the values of r for which the given differential equation has solutions of the form y = t'…

A: To find for what  values of r the given term becomes solution of differential equation.

Q: Find the Integrating Factor (I.F) of the following linear differential equation:

A: Please refer to the image below

Q: A payment of $6,500 was made into an account at the end of every 3 months for 12 years. a. If the…

A: Given

Q: २ -2 el dy ely +2 e. 2

A: To integrate.

Q: d [x² +1] dx x4 d dx -[(x² + 1)5⁰]

A: Topic = Derivative

Q: Find the absolute extremum values of f(x) = xe²-2x² on the interval [0, 1]. (Note: ez ≈ 0.22)

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Q: Use the first principles definition of the derivative to find f'(x) where f(x) = √x

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Q: 3 sin³ (tan √x² + 3x²)] dx d [(x²+1) cotx dx 3- cos x csc x

A: To find the following derivatives.i ddx3 sin3tan x2+3x2ii ddxx2+1 cot x3-cos x csc x

Q: IV. A small business determined that the price-demand and cost functions for producing and selling x…

A: This question is related to profit and cost functions, we will solve it using given information.

Q: w = 4x + y² +2²³₁ x = ers²₁, y = 1 y = In(r+s).

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Q: lim x→0 sinh x2 – x2 sinhx−x

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Q: Let f(x) = e2sinx 1. Find the absolute extremum values off on the interval [7]

A: To find the extreme values of given function at given  interval.

Q: Find the volume of the solid that results when the region enclosed by y = √√√x, y 0, and x = 49 is…

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Q: 1-10 J = exp(-x²)dx 0 Evaluate J by means of Simpson's rule with n = 2m = 10 and h = 0.1

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Q: Calculate the amount of money Cynthia had to deposit in an investment fund growing at an interest…

A: To find out the amount of money that Cynthia has to deposit.

Q: 5 Evaluate F.ds over the surface S defined by x² + y² + z² = 4 for z ≥ 0 and bounded by x = 0, y =…

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Q: Evaluate the integral: 1 - coth² (log₂ x) S² x cosh(log₂ x) dx

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Q: Use substitution to evaluate the definite integral given below. 1.³ (Enter an exact answer.) Provide…

A: We have to solve the given definite integral

Q: III. Let f(x) = e2 sinx 1. Use the local linear approximation of f at x = 0 to approximate…

A: Given problem:- Let f(x)=e2sinx.   1. Use the local linear approximation of ƒ at x = 0 to…

Q: Find the are a of the region bounded by the given 1) sketch the area, ii) Determine the boundaries a…

A: This question can be solved using the concept of area under curves.