lim x →0 Jn (x). x" 1 2″ T(n + 1) ¹ where n>- 1.

Q: 3 of |xi

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Q: √√₁²1² (2 In(x)-3) dx using six subintervals of equal width and one of the following. (Round your…

A: We just use the basic definitions

Q: Using R.K. method of fourth order, find y(0.8)correct to 4 decimal places if y'-y-x v(0.6)=1.7379

A: Given y'=y-x2  y(0.6)=1.7379. Using R.K method of fourth order, we need to find y(0.8)  The solution…

Q: du LI+ )(1 + tan"! v) 19. (1 + v²)(1 + tan v)

A: Since you have asked multiple question, As our policy we will solve the first question for you. If…

Q: 64 8. f(x) dx = 14, find xf(x?) dx. If f is continuous and %3D

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Q: 00 Evaluate "(1– x)e¯* dx.

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Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

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Q: The point P(x,x) moves on the curve y=x so that the x coordinate of P is increasing at a constant…

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Q: ()- d - en In x (en In x )(n)| = n(x")(x=l) = nx"-1 87. dx

A: Given information: The function enlnx Chain rule of the derivative, ddxefx=efxddxfx

Q: S* (1– x)e* dx

A: To find out the integration.

Q: x" – x" + 4x' - 4x = 20Cos(21) x(t) = ? =>

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Q: 3. (a) The velocity of a moving object after t seconds is given per second. Calculate the…

A: We have to find the following given condition

Q: true or false

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Q: Find the area under the curve Y=2x-3 from x = 8 to = t and evaluate it for t=10, t = 100. Then find…

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Q: e" dx Find (ez +3)(e –5) Find S In(x)x²dx.

A: The first question can be solved using the concept of partial fraction and the second question can…

Q: Solve 2 x*]1(x)dx Where Lo(1) 0.7652 (2) |0.2239 L(1) 0.4401 |L(2) 0.5767

A: We need to solve integral.

Q: 1/e -1/2 S 10x*-2(1-x²). exact value of dx 1/2

A: Given that

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

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Q: Use integration by parts to show that for n ≥ 1, we have [(lnx)" = x(lnx)" − n [(lnx)^-¹ da.

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Q: f(x) = + In(x) exp(x) + exp(-x) herex e [1, 5]. Use 5 nodes to uniformly cut the interval [1,5] into…

A: Note- Since you have asked multiple question, we will solve the first question for you. If you want…

Q: Let f(x)=x²-3x - 2380, x>0.75. Find the value of df-1 dx df-1 At x = 0, dx (Type an exact answer in…

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Q: T/2 gral S

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Q: d y Suppose dx? =D4 sec2 (2x) tan(2x), y'(0)=4 and y(0)=-1. (a) Find a formula for y' (x). (b) Find…

A: The given differential equation is  d2ydx2 = 4sec2(2x).tan(2x) y'(0) = 4 y(0) = - 1

Q: 3 2x 11-8 n x³ + 1/ 5 where [ ] = G.I.F If lim /2n dx = k, find the value of [1] + 2013.,

A: Solution :

Q: x3 - 1 Let f(x) then f(x) is %3D Зx + 1 O(x²)

A: Big O notation: If fx is a real or complex valued function and hx is a real valued function, then we…

Q: Suppose X and Y are i.i.d. Exp(A = 1). Find Pr(X +Y < 2). (a) 1/e? (b) 1- (1/e?) (c) 0.5 (d) 0.406…

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Q: I11 = +∞ -X e-* sin(2x) dx

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Q: x² + 4xy + y² = 13, (2, 1)

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Q: 2 '2 Given that f(x) dx = 7 and f(x) dx 8, evaluate the following. %D (a) f(x) dx '2 (b) f(x) dx…

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Q: ii. x² Inx dx L, x³ (e* – e¯*) dx

A: Disclaimer: Since you have asked multiple questions we will solve the first question for you. If you…

Q: cosh (x – 3) dx 8 – cosh² (x – 3) 18. 12

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Q: 2. Use integration by parts to establish the reduction formula: Sx" cos x dx = x" sin x – n x"-1 sin…

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Q: (2-2x) dx = 4, and 2-2x>0 when -1 sxs 1. Use this information and the principles of net signed area…

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Q: •15 Let * f(x)dx = 7, f," f(x)dx = 10, S f(x)dx = 3. %3D Find S f(x)dx = and S (7f(x) – 10)dx =

A: Given ∫915fxdx=7,∫911fxdx=10 and ∫1315fxdx=3. To find:∫1113fxdx and ∫11137fx-10dx. Solution:…