1. Jx cos 3x dx Sx² cos x dx 2.

Q: determine which statement is true {(x, y)|x = y2} (A) not a function (B) function; domain: R (C)…

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Q: A. y = 2e* – x – 1 B. y = 2x° – 2x – 2 C.y=e²x+x – 1 D. y = e* + x + 1 f) xy' = 1 А. у %3 4 +x Inx…

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Q: 1. Find the Fourier Transform of - 1 1 f(t) = -1

A: As per the guidelines I can solve only first question

Q: Use the mean value theorem to prove the inequality for all a and b: Isina – sinb| < |a - b|.

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Q: III. Find the area of the regions bounded by the curves. Draw a figure showing the region. 8. y =x;…

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Q: Question An open-top box is to be made from a 12-inch by 42-inch piece of plastic by removing a…

A: An open‐top box is made from a 12‐inch by 42‐inch piece of plastic by removing a square form each…

Q: A forest fire covers 1600 acres at timet = 0. The fire is growing at a rate of 2/t acres per hour,…

A: How many acres are covered 20 hours later ?

Q: acceleration due to gravity.) x(t) = ft

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Q: Determine a. (Give your answer as a whole or exact number.)

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Q: Describe the graph of the equation. = (6 – 31) i – 8t j O It is a line in 2-space that goes through…

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Q: c) y' = 3y + e* A. y = e3* – e/2x C. y = 2e³x – c²"/x B. y = ex – c/2 D. None of these d) y' = cos x…

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Q: CORRECT

A: We have to choose the correct option from the given options according to the given information

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4v1 +…

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Q: Find the nth derivative of y = In(16x2 – 9).

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Q: A farmer wants to enclose a rectangular field with area 1,000 square meters by fencing it into four…

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Q: che unit sphere does the following in

A: We have to choose the correct option from the given options according to the given information

Q: Fina the integral (2x-1) (x+3) a. In 7 (2x-1) + C x+3 b. In 6 (2x-1) + C x+3 3 (2x-1) c. In + C x+3…

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Q: For the series E=13 * a. Find the first two partial sums si and s2 b. Does the series converge, and…

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Q: Consider a triangle where A = 30°, a = 1.5 cm, and b 1.2 cm. %3D (Note that the triangle shown is…

A: Explained below

Q: g Ca) : -8) (uring logarithmic differentiation) 2 +4 11

A: We can find the derivative using logarithmic differentiation as below.

Q: Frod the averuge vearlue of the durndkam f over Shoe lad eraual [q,9]

A: Solve it

Q: Solve the given equation.. (3x2 + y)dx + (x²y – x)dy =0 Y +3x = C a. b. x²y? + x²y+ x4 = C C. d.…

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Q: Find the total area of the region between the x-axis and the graph of y = -x - 3x, - 6sxs1. The…

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Q: Use the given information to find the indicated probability. An B = Ø, P(B) = 0.1, P(A U B) = 0.1.…

A: Solution - Given:-  P(A U B) = 0.1 ,  P(B) = 0.1  P(A) = ?

Q: re (in radians). Slope of Terminal Ray = 0 0 = 6.28 If 0 = 1.3, what is the slope of the terminal…

A: Topic:- trigonometry

Q: Find the derivative of the function. f(x) = In x+ 2 f'(x) =

A: We have to find the derivative of the given function.

Q: A ball is thrown vertically upward from the top of the house 112 ft high with an initial velocity of…

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Q: 8. 21

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Q: 4. Find the arc length of r = cos? (0/2), 0 s 0 s 2n.

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Q: A tangent line to the curve c(t) - (- 4t - 5t + 2, t - 15t - 1) has slope 3 at the pointias) 2-1…

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Q: Given f(x): find the average rate of change of f(x) on the interval 8, 8+ h. Your answer x + 8 will…

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Q: An approximate

A: answer is in next step

Q: d. q(x) = cot-1 ( ) 1-nx

A: Follow the procedure given below.

Q: An iron block weighs 5.2 N and has a volume of 272 cm³. What is the density of the block in kilogra…

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Q: 21-23 Use Definition 2 to find an expression for the area under the graph of f as a limit. Do not…

A: To solve the following problem s

Q: Find the inverse Laplace transform of 5s + 1 F(s) = s2 – 7s + 12

A: F(s)=5s+1s2-7s+12       =5s+1s2-3s-4s+12       =5s+1s(s-3)-4(s-3)       =21(s-3)-16(s-4)(s-3)(s-4)…

Q: 1. Find the derivative of the following: (Simplify your final answers.) sech h. j(r) = e (Using…

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Q: 1 q(x) = cot-1 ( V1-πx2

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Q: dV = vt+1+t where V 4. The volume of a balloon is increasing according to the formula dt cm³ is the…

A: To solve the given differential equation and find an expression  for V(t).

Q: What is the derivative of f (x) = 3x³+2x using the limit definition (please use delta x if possible)

A: A detailed solution is given below

Q: A ball is thrown vertically upward from the top of the house 112 ft high with 6. an initial velocity…

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Q: When harvesting apples in a grove, the number of apples harvested increases at a rate of R(t) apples…

A: Here, the rate of harvesting increases at the rate R(t) per hour with t≥0

Q: Can the following limit be calculated using L'Hopital's rule? x + cos(x) lim x→ 3 x + sin(x)+2 If…

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Q: Let h(x) = x3. Use the Intermediate Value Theorem to show that there is a number between 2 and 3…

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Q: The volume of a cantaloupe is approximated by V=za. The radius is growing at the rate of 0.8…

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Q: dx 29. Evaluate + sinx + cosx c) h|1- tan | +C D) tan{1- tan +C A) tan 1+ tan +C B) h1+ tan +C

A: To Find : ∫11+sinx+cosxdx     Note : a)  1+cosx=2 cos2x2b)  sinx=2sinx2cosx2

Q: Question 5 Find the volume of the solid that results when the region enclosed by the given curves is…

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Q: Find all the derivatives of f, given f(x) = x3 - 5x' + 4x6 – Tx* + 3x3 + 11.

A: This is a basic derivative problem

Q: Use the limit definition to compute the derivative of the function f(x) = Vx + 2 at x = 1. (Use…

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Q: M Problem 1. For the function f whose graph is given below, list the following quantities in…

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