b) f(x) = e-2x – x In x + x – 7 e*-e-x c) f(x) : ex+e¬x

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Q: integral from 1 to 2 of (e1/x^3 ) / x4

A: To evaluate

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A: First break by using partial fraction then integrate

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Q: Let f(x) = 16 ln( – x) + 4x + 13. (a) f'(x) = (b) Solve f'(x) = 0 to determine the critical values…

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Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

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A: 2

Q: A b B d a The integral 15x²x³43x - 19 (x + 1)²(x² - 6x +13) can be rewritten as Ax + B D C + ax² +…

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Q: 1 Evaluate the improper intergal | dx (x2 + 9)° using the residue theorem.

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Q: 1. Evaluate the limits. e' cos (t – 4) dt - 4 (а) lim x2 x2 – 4 e2 + 2 (b) lim x00 e2x + 100

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Q: the Fundamental Theorem of Ca -5 (x³ – 9x)dx. v3

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Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: 2 3. Evaluate the integral ||x dx -2 O 2 4

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Q: S de x² –2 x+1 A x2 --x - In Ix + 11 + C C x2 +x - In Lx + 11 + C B x² -x + In Lx + 11 + C x2 +x +…

A: Given ∫x2-2x+1dx. The objective is to evaluate the integral.

Q: Evaluate the integral dx 2x리x-3월 x2 1 3 + V2x In A + C 2/3"3 - V2 | ® In(2x x - 3{x²) +c 1 In + C…

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Q: 8. Compute using the trig. substitution S x2 -dx (1–x²)1/2

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Q: | 45. Apply integration to the expansion 00 =E(-1)"x" = 1- x+x – x +.. 1+x n=0 to prove that for -1…

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Q: 1. Find an antiderivative of f(x) = 16–x². Then, use The Fundamental Theorem of Calculus %3D 4 to…

A: Given : fx = 16-x2

Q: (6) Find the indefinite integral (af* -3x +2 Fdx x+1 12x - 22x (bJ -dx 3x* -11x +15 x² + 2x +3 -dx…

A: Note: As per companys policy we should do maximum 3 subparts of a question.So, kindly post the other…

Q: Find the linearization of y = ev7x at x = 16. (Use symbolic notation and fractions where needed.)

A:

Q: 9-x2 B: Find the integral S 18-x2-y xydzdydx.

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Q: 12. Find the general solution using Reduction of Order: a) y" = In x

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Q: Use Dirichlet's principle with n = 10 to find a rational approximation of T.

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Q: Find T; (x): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = 0. T3(x) = %3D

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Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy =yx.

A: Since, yz = zxy

Q: Consider the IVP S2(t) = -1+cos(t + x(t)) cos(t + x(t)) x(0) = 0. Show that the ODE is exact and…

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Q: 19. f(x. y) In(1 - x - y) %3D

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Q: – 30 - Evaluate the integral: -d.x x2 Vx2 + 16

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Q: 3 Evaluate the definite integral dx. (x- 5)4 -2

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Q: 1 Evaluate the improper intergal dx (x² + 16)² using the residue theorem. 8.

A:

Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

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Q: J arctan x dx A C In(x2) + C In(x² + 1) + C x arctanx x arctan X - | 1. x arctan x +- In(x2) + C x…

A:

Q: 10 Evaluate the integral f 2x (x2 + 4) " dx using the substitution u = x² + 4. 2x (x² + 4)*" dx =|…

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A:

Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

A: Solve the integral  √(x2+25)/9x2

Q: Compute f'(1) where f(x)=1/2 e-2x + ln(x2 + 1)

A:

Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy = yx.

A: Assume that x2 = y2 = e and yz = zxy.  Now from  yz = zxy we have  yz-1 = zxy-1z-1y-1 = y-1 x-1 z-1…