What is (cos x + x) dx? O-½ sin²x + x²/2 + C ○ -sin x + x²/2 + C O sin x + x²/2 + C O. ½ sin²x + x²/2 + C

Q: What is the difference between Rolle's Theorem and The Mean Value Theorem? Explain

A: See the details solution in below

Q: 2. The function ƒ(x) = x² − 4 is transformed to g(x) =— (x² − 4). Compare the domain, range,…

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Q: Evaluate the function at the given values of the Independent variable. Simplify the results. g(x) =…

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Q: Using Desmos or other graphing software, sketch the graph of y = sin (2x). a. Using the tangents,…

A: Y=sin(2x)

Q: integral

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Q: If r(x) = -cos (x + 9) +7, determine the antiderivative of r(x). (Do not include the constant C'in…

A: In this question, we want to find the antiderivative of the given function r(x).

Q: How did you get 6?

A: For a horizontal asymptote to exist for a rational function, the numerator has to be of the same…

Q: What is the gradient of f(x, y, z) = x³₂² + y³z +125z - 1 at P(5,5,-1) ? 75i + 75k -75i - 75k 75i -…

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Q: ƒx(2x−1) dx 2 √x³√x²+4 dx

A: for (1),     ∫ x2x-17dx=∫ 128x8-448x7+672x6-560x5+280x4-84x3+14x2-xdx=∫ 128x8dx-∫ 448x7dx+∫…

Q: Find an angle coterminal to  25π/3 that is between 0 and 2π

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Q: A local club is arranging a charter flight to Hawaii. The cost of the trip is $543 each for 83…

A: We need to find no. of passengers and max. revenue.

Q: Find aw/as and aw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) x = s+t,…

A: We can answer both the answer as below.

Q: Sx tanx dx

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Q: 3) y" + 4y' + 4y = 0.

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Q: Evaluate each expression based on the following table. X f(x) (a) f(2) - f(-2) (b) f(-1)f(-2) (c)…

A: To evaluate the given expressions.  From the given table.

Q: • У -ky = 19.2 2 + воё, усо) =ўс 4Х -ЧХ 4X Ans: Y = 22ë + +24xе X -Че

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Q: The function is not one-to-one. Delete part of the domain so that the function that remains is…

A: Here we have to find the inverse function.

Q: Find f if f"(x)= e-sin z - 3 4√ f'(0) = 0, and f(0) = 8.

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: Find the directional derivative of the function at P in the direction of v. 1 = √₂ (i+j) f(x, y) =…

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Q: a ht C1 For the function f(x,y) = 4x² + 7y², find the following. a. b. f(x+h,y)-f(x,y) h…

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Q: Find the limit of s(n) as n → ∞0. ( s(n) = 4 n n(n + 1)(2n + 1) 8

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Q: (b) Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: Diminishing Returns Jesaki Inc estimates that it will sell N(x) units of product after spending $x…

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Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: Write an equation for the function graphed below. The y intercept is at (0,0.3) 5+ 4- 3 5-4-3 1 1 2…

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Q: 2. Given the function f(x, y)=3x²y + 2xy-y, a) find the value of the directional derivative of the…

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Q: at ch Use the Fundamental Theorem to show that the following is true. a f b C b [ f(x) dx = ff(x)dx…

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Q: | (8z + 4z³ - 6z²) dz? O 16z²+z4-2z³ + C O4z²+z4-22³ + C 16z²+z4+ 2z³ + C O 42² +224 + 2z³ + C

A: Solution: ∫8z+4z3-6z2dzApply the sum rule=∫8zdz +∫4z3dz -∫6z2dz

Q: Verify the identity. 1 - cos(a) sin(a) 1 - cos(a) sin(a) sin(a) 1 + cos(a) 1- cos(a) sin(a) 1 1 +…

A: Given,…

Q: (a) Determine whether the series n=1 n+1 n³ +3 is convergent or divergent.

A: Solution: ∑n=1∞n+1n3+3

Q: Determine the graph of the equation. -x² - y² =z Choose the correct graph of the equation. O A. at…

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Q: For the function f(x,y,z) = x rr fy 11 he e = 11 f₂ = N fyz 10 8z+1 -9 8z+1 (9y-10x)8 (8z+1)² 11 72…

A: The given function is;  f(x,y,z)=(10x-9y) /(8z+1).

Q: Find the general solution of the given higher-order differential equation. + 3y" + 3y' + y = 0

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Q: Suppose that you have measured the length of the side of a cube as (3.00.005) meters. Give an…

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Q: What is the directional derivative of f(x, y, z)= In x 2 + 2y2 + 4 z 2 at the point P(-1. 2, 4) in…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Explain why x ≤- 2, 0 ≤ x ≤ 5 could not be the solution to (x-5)(x+2) ≤ 0.

A: This question is based on solution of inequality.

Q: 2 Solve the following ODES by Inverse Operator method. (D²³+1) y = 3+²+52x Ans: y = c₁e²+ ¹² (C₂…

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Q: -6-5-4-3-2- 9 10

A: We will solve.

Q: нх У - 169 = 19.2 ё + воё, усо) =ўс) 4Х 4X -4Х Ans: y=2.2 +e+24xe X - Че

A: Solution of given question is written in below steps.

Q: g(b)= g'(b)= Calculate g(b) and g'(b) where g(x) is the inverse of f(x) - 18, where b=4 248

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Q: Find the gradient of the function at the given point. g(x, y) = 12xe/x, (12, 0) Vg(12, 0) =

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Q: The top of a ladder that is 5 m long slides down a vertical wall at a rate of 2 m/s. At what rate…

A: Given :Length of ledder=5m

Q: -y(2x+y) x(x+2y) - y'=-

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Q: Find f(x+h)-f(x)/h for the given function . f(x)=x2+8x

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Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: Consider the function f(x) = √x. (a) Find the first and second Taylor polynomials for f at x = 1 .…

A: Given : taylor series =fx=f(x0)+f'(x0)(x-x0)+f"(x0)(x-x0)22!+..........     first taylor polynomial=…

Q: Solve the following ODES by Undetermined Coeff 11 X 4X y 16 y = 19.2 € + 60 e - , уса) =ўс=0 THY 4X

A: This is a problem of ODE. Please follow the procedure given below.

Q: Solve the following ODES by Undetermined Coeff. 17 4X y - 16 y = 19.2 e + 60 e ycolý 4X -4X Ans:…

A: The given differential equation is;  y''-16y=19.2e4x+60ex y(0)=y'(0)=0.