5 Given that f f(x) dx = 13, evaluate the following integrals: (a) f3 f(r) dr = 3 (b) f f(x) dx (c) f., 7 dx (d) fs (10 f(x) - 7) dx = =

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Q: 23 Evaluate the determinant 7 2 - 3 4 5 -2

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A: given  F=8i-6j+9kobject moves from (0,6,8) to (6,12,22) formula for work done is W=F.drwhere dr is…

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Q: dx (7) If f'(2) = 5, then dx (4f(x) + x³)|x=2 : (A) 12 ✓ion (B) 4 (C) 20 (D) 32

A: We use ddxfx+gx=ddxfx+ddxgxddxkfx=kddxfx

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Q: 7 -6 -5 -4 -3 -2 -1 5 4 3 2- 1 -1 -2 -3 -4 I 2 3 4 5 e

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Q: Find the particular solution to the differential equation (dy/dx)=(x-5)e-2y satisfying the initial…

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Q: 3. (Lines and Planes) Consider the intersecting lines, L₁=3-3t, y=t, z=0, L₂-3s, y=0, z=2+28.

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Q: 8 2/7 4/7 5/9 3/5 x² - 4x +3 x+3x²+x-12° Calculate lim

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A: Given curve Equation:- y=x-1x-32

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Q: (c) y = e-t - 3y, у 1 e 2 - е -3t

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A: Given that , ∫0a2xdx=2023 find the value of a.

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A: The light in the lighthouse rotates through one complete rotation once every 4 seconds.

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A: first of all plot the graph by using any graphical tool (demos)

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A: Given that,          f(x) = 3x2+3x+4 we need to estimate the area of f(x) from x =3 to x =9 using…

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Q: Q2: Calculate the shortest distance between the two lines: (2) a-L Zo z+1 and a

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Q: K Construct a table and find the indicated limit. √x+2 X-5 If h(x)=- Complete the table below. X…

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Q: 19. Find the general solution of (D4 + 6D³ +9D²)y = 0. 2 a. y=C₁ +C₂x+C3x² + c4e³x C46 Y = C₁ + C₂x…

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Q: 2) Is f(x)= x²+1 if x<1 4x-3 if x ≥1 differentiable at x = 1? Justify.

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Q: Verify that λ; is an eigenvalue of A and that X; is a corresponding eigenvector. = λ₁4, x₁ = (1, 0,…

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Q: 7. Determine values of a, b, and c such that the graph of y = ax³ +bx² + c has a local extremum at…

A: To determine the values of a, b, and c such that the graph of y=ax3+bx2+c has a local exremum at 2,…

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Q: (11) The value of a such that 6+ dt = 2√x is: (A)3 (B) 6 (C)9 (L

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Q: (12) f(secx) (secx + tanx) dx =: (A) tan(x) + sec(x) + C (C) tan(x) + csc(x) + C (B) tan(x)sec(x) +…

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Q: temperature at which water starts to boil​ (its boiling​ point) is linearly related to the altitude.…

A: Given query is to find boiling temprature at 8500 ft.

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of x 8 ƒ( x ) = √ √ ²* ( ²…

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Q: Consider the following function. = √√x8 + 1 (a) Make a sign diagram for the first derivative. f(x) =…

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Q: Question 2. The second order linear homogeneous differential equation y" + 2y' = 0, has a general…

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Q: Find the are of the region:  y=9cos(pi*x) , y=8x^2-2

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