Suppose h(x) = f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) 8 10 -4- CN F 0 I I CN -4 I I T I I 2 12 14

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A: Solution: The objective is to find the partial derivatives of the given functions

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A: Integration is evaluated.

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A: I am going to solve the problem by using some simple calculus to get the required result of the…

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A: We will solve the problem.

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Q: Find the solution of the given initial value problem. v- 7 y = y' cost t-7' y (π) = 0, t> 0 y(t) = =

A: The standard form of the first-order differential equation is: dydt+Py=Q Where P and Q is the…

Q: 5. Determine the roots of y"" - 3y" - y' + 3y = 0 a. 1, 1, 3 b. 1-1, -3 c. 1, 1, -3 d. 1,-1, 3

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A: We have to find the circulation of F→.

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A: To evaluate the integral: ∫π2π∫0u2sintudt du

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Q: Evaluate: ³₂²₁¹ [2³(x + y)³] dz dy dx

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Q: 3 By direct partial integration, Solve the following PDES 8- 8²u axdy = ceBX Cosy SXUCX,#) Ex u(π,…

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Q: Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

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Q: Evaluate: ²₁¹ [2³(x + y)³] dz dy dx

A: Topic = Integration

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Q: identify any extrema of the function by recognizing its given form or its form after completing the…

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Q: Consider the parametric curve: X = = 7et y = 3t5 Which integral gives the arc length of the curve…

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Q: Q4/Find the slope of the line 3x-4y=-8 and then find the distance from the point P(3,-2) to this…

A: Given Equation of line3x-4y=-8To find slope & Distance.

Q: Question 3 Determine L-1 ¹ s²+3s-7 (S-1) (s²+2).

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Q: Example 1: Evaluate the integral: ₁²²=238+1² 2r-3 - 3x + 1 dx.

A: The given integral is (2x-3) /sqrt(x2-3x+1), limit from 3 to 5.

Q: dx (x² +25)3/2

A: To find the integration.

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Q: (2) Z/(5) =........ (i) (5) (ii) 5Z (iii) {[0],[1],[2],[3],[4]}

A: We have to find out integer

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A: We have to find the operation

Q: Given f(x)=x²-1 on [-2,2]. a. Find the critical numbers of f on the given interval. b. Determine the…

A: A critical number of a function of a single real variable, f(x), is a value x0 in the domain of f…

Q: S f(x) dx = [ -6 -5 f -2 Y 7 3 -3 7 X

A: This above given expression of integral is shows integral value of function f(x) from x=3 to x=7.

Q: cln 3 In In 2 tanh xsech’x_dx

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Q: an+1 Suppose that an ∞ Σ απ( – 81)" man n=1 →1 as n→ ∞o. Find the radius of convergence.

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Q: The value of sin cos (x²+)+C C. cos (x²+)+C xp B. -cos (x²+)+C D. -cos (x²+)+C

A: Topic = Integration Correct option = B

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 13x)y², y(0) : =…

A: Given,dydx=(1-13x)y2                     y(0)=-16

Q: Find the area of the region enclosed by the curves y = 4 24 8 16 x³ and y = 4x.

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Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

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Q: True or False? 4. Let f : R → R be a function defined by f(x) = x^2+1. If B = {2, 5}, then…

A: according to the company rule we can answer only the first question and rust can be reposted.

Q: ./ which expression best to describe 31% ? (a) Just under a half (b) A tiny fraction (c) Nearly a…

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Q: VSDE of tan xdx + y * cos^2 ((x) * dy) = 0

A: (Sinx/cosx)dx+ycos²xdy=0 (Sinx/cosx)dx=-ycos²xdy (Sinx/cos³x)dx=-ydy tanx sec²xdx+ydy=0 Integrate…

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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