x(x² + 1)² 1. f(x) = ln 2x3 – 1 3 sin-1(x In r

Q: T/3 4 sin x -dx 1-4cosx

A:

Q: Evaluate 1 70 sin° (f (x)) cos*(f (x))g(x) dx COS where g'(x) = r for all x with g(0) = T , • f'(x)…

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Q: dx - = In[F(x)]+C•What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1) -1 + - -1

A: Solved below

Q: r sin(T|2² - 1) cos² (7|2² - 11) da -3

A: To find the following definite integral.

Q: Let f(x) = (sin(x))*. Find the value of (a) 1 (b) 2 (c) 2 (d) 2 (e) 0

A: The given function is fx=sinxx. To find the value of f'π2, first take the logarithmic of fx=sinxx on…

Q: xpress tiIE SS the f (x) = 3 sin? x + cos? x of oog m

A:

Q: Prove 3sin x-45 in ³x = Sin (3x)

A: To prove that,3 sinx-4 sin3x=sin3x

Q: (4)Evaluate the definite integral (a)(1+ si 0 1+ sin x)dx (b) (2t+cost) di (b) f( -x/2 x+ X - dx R/4…

A: Explanation of the answer is as follows

Q: 7/4 2 sec(6x)dx sin(r In(x)) 13x 1

A: (b)

Q: 68) Find a value of c that will make sin2 4x 0 x2 f(x) = C, x 0 continuous atx = 0.

A: Given,

Q: If f (x, y) = x(x² + y²)-3/2 esin(a²y) find fa(1,0).

A:

Q: 2. 1 Evaluate the definite integrals below. Use u-substitution when appropriate. 4 5 3el/x (a) (b) |…

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Q: dx For - = In[F(x)]+C• What is f(/3) if C = 0? (x+x³) (x Tan-'x + 1) -1 - 6. + -1 - -15 -is -is

A: Integrate ∫dx(x+x3)(xtan-1x+1)

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Find L {f(t)} if f(t) = cos 5t + sin 2t

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Q: Find approximate value of the derivative for f(wo)-6f(x1)+3f(x2)+2f(x3) fr(x2) = f(x) = 10 sin(20æ?)…

A: Introduction: Numerical differentiation is the technique of obtaining the numerical value of a…

Q: Evaluate the definite integral. (Be sure to show your work.) (a) / (2³ + 1)dx (sin x + 1)dx 2 (b) /…

A: Since you have posted question with multi-parts. As per guidelines, we"ll solve only first three…

Q: Let F(x) | sin (4t?) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.8 Use this polynomial…

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Q: (x² – 1) d x (x* + 3 x² + 1) tan-1(*-) dx

A:

Q: Let Find f(x) = y = f(x) = 5x + 18 cos x. d f(x) =

A: Given query is to find the derivative at indicated point.

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: xet dx (x+1)- 4.

A:

Q: 1 sin(x) (D²+1)³

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Q: dx 1 +X |1- (Tan (x) )2 12

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Q: Find f. f(x) = f"(x) = x3 + sinh(x), f(0) = 1, f(2) = 2.6 ×

A:

Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: Determine f,(x); f(x) = cos(2x³ +n²)

A:

Q: Find f"(7) given f(x) =- sin(z – 3x) our Answer:

A: Please see the below picture for detailed solution.

Q: Evaluate L{3 (t² – 1) sin (2t) + 7et cosh (4t)}

A:

Q: Evaluate (i) dx S √e xlnx√(2lnx)² – 1

A: We are asked to evaluate the integral