cosx * sin? (3x) 2 2. lim x→0 x2

Q: Q6) Evaluate the following integral by using Odd and Even Powers Method: | cos* (;x) dx y =

A:

Q: If the solution to ſe2* sec²(e²×+1)dx is equal to k tan(e2x+1) + C , find the exact value of k.

A: We know, ∫sec2(x)dx=tan(x) ddxemx=memx

Q: (-4x-12) dx (x+10) (x-4)- For F()- 1. What is F(3)? %3D

A: Option A

Q: landscaping

A: We will find a linear equation. 

Q: Use the ratio test to determine whether the series converges or diverges. If the test is inconclusiv...

A: Given series  ∑k=1∞5kk!

Q: Evaluate the integral. In(9 x - 8) dx =| +C %3D

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Q: 1- 8x + 72(-1) (k + 7)! k! k=2

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Q: (-4x-12) dx For J x+10)³ (x-4)³ F(x) – 1. What is F(3)? -

A: Given: ∫-4x-12x+103x-43dx=Fx-1   ...(1)  

Q: Find the derivative of y with respect to x for y = sinh 1(11/15x). dy 165 dx 2/1815x? + 15x

A: Given query is to find the derivative of the expression.

Q: 9 Evaluate xp.

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Q: The integral / 2/ ) cos(2*) dr takes the form & cosu du when u=2* and f (x) =x-5, What is the value ...

A: Firstly We have to solve the integration, then compare to given form and find k. Then We get K+2.

Q: Evaluate the integral. 3 sin x dx +C |3D

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Q: Given f(x)-3X+l evaluate (f'o f(s)) 1-SUEJEC

A: Given: f(x) = 3x+1 For (a), Let y=3x+1.Replace x by y,    x=3y+1⇒y=x-13 So, we get f-1(x)=x-13. Now,...

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

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Q: Find The artlal Auatives (first and Seond

A: Since the student has posted multiple questions and does not mention any specific question, so we ar...

Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

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Q: Find the differential equation whose solution is given by y? = 4ax ydx – 2xdy = 0 O ydy – 2xdx = 0

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Q: S(x) = Vī – 8 VF f "(x) =

A: Given, fx=x-8x3 We have to find f'x.  

Q: Find the indefinite integral. (Use C for the constant of integration.) |zV 16z2 - 81 zp

A: ∫1x2+a2 dx = 1aarc tan(xa)+C

Q: The function f(x, y) : 1+2? +y? is 1-x2 -y? discontinuous at the points {(x, y)\æ² + y² # 1}. True F...

A: f(x,y)=(1+x^2+y^2)/(1-x^2-y^2)

Q: Given: 5x cos 3x dx. If u = 3x, then the resulting integral is f(u)du. Find f ): 5/2 18 18 5/2 12 5/...

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Q: Practice: Find the volume of the solids generated by rotating the area bounded with the given functi...

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Q: FIII in the yellow box to complete the truth table of "p v (q →r) V q->r "p v (q →r) r 5.

A: Concepts:   ~ p is oppostite of p.p=T then, ~p =Fp=F then, ~p =T   Implication Truth table:   Disju...

Q: Q2) Show that y = 35 x* – 30 x² + 3 satisfies ( 1– x² )y" – 2xy' + 20y = 0 %3D

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Q: EXERCISES 1. What value(s) of c, if any, will satisfy the IVT for the given function f and the given...

A: topic - intermediate value theorem

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

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Q: Consider the integral 2n* g(x) dx . There is a function g(x) such that when u = In x the resulting i...

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Q: Given h(s, t) = s In t – t ln s. What is the value of h(e, 1)? %3D

A: topic - functions

Q: m+2m Consider J dm. If we letu = m+ 1, what will be the resulting integral as a function of u? In(u)...

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Q: Suppose x = 6, 0 = 4 radians and ø 8 radians in the figure, which is not drawn to scale. Determine t...

A: x =6 θ = π/4 so apply trigonometric function tanθ = y/x y = xtan(π/4) y = x y =6 for right angle tri...

Q: Solve the following differential equation y = - 3x²sec²(-x² - y) Select one: Oa. +C O b.(-x-y)- sec°...

A: In this question we have to solve the differential equation.

Q: The integral / 2/ (*) cos(2*) dx takes the form k cosu du when u=2* and f (x) =x – 5. what is the va...

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Q: Set up a definite integral with respect to y (dy) (set up only, do not evaluate the integral) to fin...

A:

Q: B= 4 7 8. A= 2. Find 1-Matrix C. 3B 2- Matrix D - AB inNN

A: Given A=352252 and B=204768C=3B=3*204768               C=[6012211824]

Q: Determine f(x) so that | cos(In?x) f (x) dx = sin(In?x) + C

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Q: Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polyn...

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Q: Given A=3az +3ax -2ay, B=2ay -ax +5az, C=3ax +2az +2ay and D=-ay +3ax -2az. Find scalars a, b and c ...

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Q: 2. Given: a1 16, а4 1024 Find: az =? а. 12 b. 18 с. 36 d. 64

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Q: e3x Let dx be given . If u = e* + 1, then the resulting integral is S f(u) du. Compute f(3). ex+1

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Q: Question 4 (2x* +)x J (x8 + 4x5 + 4x²)² Using u-substitution and transformation of the integrand, th...

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Q: If u = f(x), then S k dx = +C for some constant k. Compute kf(1). %3D x*+2x2+1 x2+1 4 -1

A: u=f(x)f(x)=xx2+2I=∫ xx4+2x2+1 dxI=∫ x dx(x2+1)2u=x2+1du = 2x dxx dx =du2

Q: Jse the binomial series to find the Maclaurin series for the funct 1 f(x) (1 + x)³ %3D (x) =

A: Given: f(x)=11+x3

Q: Which of the following is true about horizontal asymptotes? OAll rational functions have at least on...

A: Find your answer below 

Q: dx The integral S reduces to S k, where u = f(x) and for some constant k . Compute f(1). ex+1

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Q: prove that (sin?acos'x)(tan?x+ cot?x + 2) = 1

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Q: If cotx 12 find the other trigonometric functions

A: topic - trigonometric ratios

Q: хdу + (у — ху + 2\dx — 0 %3D

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Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

A: To find: The value of dydx in terms of x and y. Given information: y=csct,x=sec-1t  

Q: (e) S (x2+4x+5)2 d.x

A: To integrate: The integral ∫x+1x2+4x+52dx.