( 2 + x², -2

Q: 3. f (x) = x² + 5x + 4 3. f (x) = x² + 5x + 4 Opens up/down: Vertex: Axis of symmetry: Solution(s):…

A: The quadratic function is a second-degree polynomial in which the highest power of the variable term…

Q: A-f cos (x)sin³(x)dx e*cosh (3x) B-J cosh(x)+sinh(x)

A: Here we use use substitution method to evaluate the given integral.

Q: 26. Solve using integration by parts f x*e-3* dx. Show your solution

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Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

A:

Q: 25. Solve using integration by parts f x² Vx – 1 dx. Show your solution.

A:

Q: 5. Solve using integration by parts f x² Vx – 1 dx. Show your solution.

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Q: f(x) = 2 arctan x + x f(x) = In(x? - 4x +5)

A: Solve the following

Q: 9) Find all relative extrema in the interval (0, 2π) for y = x - cos x

A: Here we have to find the relative extrema.

Q: 9. f (x) = x² – 8x + 12 9. f (x) = x² – 8x + 12 Opens up/down: Vertex: Axis of symmetry:…

A: The quadratic function is a second-degree polynomial in which the highest power of the variable term…

Q: f(x) = -(x ² + x-30 (x, f(x) Axis of symmetry: ● X-int (smaller) x-int (Larger) Form: Standard •…

A:

Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

A:

Q: 9. 2x-1 (x+1)(x-2)² -dx

A:

Q: V3x-e2x-(x ln x)(ln(ln x))| In(ln x) Given a function, y = dy Show that dx V3x-e2x (x In…

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Q: Lim x-0 e³ +ex -x²-2 sin² x-x²

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Q: 4. Interval 0<x<n, function, f(x) = sin 2x. %3D

A: We have to find the Fourier series of the function fx=sin2x ,x∈0,π

Q: 2х -3 -dx. Evaluate(x-2)(x² + 1)

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Q: 5.5x-2 dx

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Q: Example: Use the Secant method to estimate the root of f(x) = e-x-x. Start with initial estimates…

A: To use secant method to estimate the root of fx=e−x−x

Q: 8. f(x) = 2x² – 4x + 2 8. f(x) = 2x2 – 4x + 2 - Opens up/down: 10 Vertex: Axis of symmetry:…

A: Domain are set of values for which the function exists.

Q: dx x+x4/3

A:

Q: (4x-2)dx x³-X² - 2x

A: We have to evaluate ∫4x-2 dxx3-x2-2x.

Q: Limit -1 to 1 integral (1-1/2 x) dx

A: Given:        ∫-111 - 12x dx   To find the value of ∫-111 - 12x dx   Formula:          ∫xn dx = xn…

Q: 3. y = (- at x= 3 x+1

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Q: Hn+1(x)= 2x Hn (x) – 2n H-- 1 (x) H,(x)= 2n Hn-1(x).

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Q: (x²-2 (a) f(x) = 4, (sin 2x x + 2 (b) f (x) = { 1, x-2 at x = 2. at x = 0. X = 2 x = 0

A: A function is continuous at any point x=a if it satisfies the below condition. LHL=RHL=fa LHL is the…

Q: Che number ofunits in Z31[x] is

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Q: 10 If f (x) dx -7 and f (x) dx = 1 then determine -3 -3 10 [1- f(2) dz 5 showing working.

A: Given: ∫-35f(x)dx=-7 and ∫-310f(x)dx=1

Q: x*sin (2x) dx a. ** cos(2x) – x³ sin(2x) –r² co. 3 x² cos(2x) +x sin(2x) +- cos(2x) + C 4 1 cos(2x)…

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Q: (a) Using integration by parts, find fx sin(2x - 1) dx. (b) Use substitution method to find x² 2x-1…

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Q: (x²–1)dx S (x++3x² +1)[tan-1 x2-1 aluation of is

A: Given integral is I=∫x2-1x4+3x2+1tan-1x2+1xdx To evaluate I Now, dividing the numerator and…

Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

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Q: 9. f √x³-1dx x

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Q: Proove: Yn- n-1 x

A: Given That : Let us assume that  y=xnlog(x) Prove that : yn=n!x using Leibnitz  theorem

Q: 1-2 c) dx

A: Evaluate the integral: ∫01e1-xdx. Simplify- ∫01e·e-xdx Apply ∫afx dx = a∫fx dx here a is constant.…

Q: 20. (x-2x³+1)dx (x² - 2x+5)

A: I am attaching image so that you understand each and every step.

Q: sech x+csch x Q3: prove that e2x %3D csch x-sech x

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Q: 1.) lim 2x sin'x. *P0 ex - x - 1

A: We apply l- hospital rules and solve it. Follow 2nd step.

Q: *n/3 27. tan'x sec*x dx 28. tan (2x) sec (2x) dx /3 29. tan'x sec x dx 30. tan'x sec°x dx 31. tan'x…

A: solve integration

Q: (sin(x), x 4 x, k(x) = f(x) = -x2 + 4x – 2, х — 6,

A: Consider the given function as fx=sinx     x&lt;0x         0&lt;x&lt;2-x2+4x-2…

Q: lim COS X tanx メー→o <-2メ4リX-8 2lim 3 メ→ 2 xリ_2X メ-2 xツ_2Xメ

A:

Q: Find the limits

A: Given,                     lim(x,y)→(0,ln2)ex-y     And we have to find its limit.

Q: dx (5-4x-x²) 18. 8. f

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Q: V1+ sin (x5) e-y 2(Vx- 1) f-- cos {sin(2x*)} x-2 x2+3x

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Q: 5-7 -1 Using quotient rule, show-that d [cotx] dx 2. 1+x

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Q: 1+ tanh x e 2x 1- tanh x

A: Prove the following Use the identities

Q: 3 Find the maximum and minimum values for f(x) = - 4-(/2 cos x - V2 sin x)

A: Topic = Functions Maximum value of f(x)=1.5 Minimum value of f(x)=0.5

Q: x*cos (x²) 1 – cos 3x lim X-0

A: we have to find the limit of the given expression

Q: 1. lim 3r+2r+1 X-n Sx2+7x+4 2. lim +sinx

A: See 2nd step

Q: cos(2x)- sin(2x)cos(2x)) cos(x)- sin(x) dx = -F(x) + For C. What is F (x)? 3.

A: