6. Let f(æ) = x² and g(x) = ln(x). Then f(g(x)) is: Select one: O n(x?) In (In(x)) a² In(x) O (In(x))² O 2 In(x)

Q: 8. If g(x) = e*In(x+1), compute g'(x). What techniques are you using in this case?

A: Solution is given below..

Q: 1 4. First, make a substitution and then use integration by parts to evaluate [Hint: Use the fact…

A:

Q: 2- Find O for: y= In (x+5x) dx

A: Tpoic- Differentiation

Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

A:

Q: In ( ;). Find for. z = ln Əz Əx

A: Given that       z = ln(x/y)

Q: find the absolute extrema of thefunction on the closed interval. y=x^{2}-8 \ln x,[1,5]

A: Given:- function y=x2-8 Inxdefined on the interval 1, 5 The derivative of the function is y'=2x-8x…

Q: Find the linear approximation of f(x) = lnx at x = 1 and use it to estimate ln(1.02). L(x) =…

A: Given that: f(x)=lnx

Q: 4. Suppose fand f'are differentiable functions of x. Given f' (4) = 0, f" (-), and g(x) = (). log…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: 73. Use the definition of |x\, the chain rule, and the fact that (In x) = - for x > 0 to prove that…

A: Given, dlnxdx=1x, x>0 from definition of x x=x ,     x>0 -x ,  x<0  if x>0 then d…

Q: In(x²+x)-In x+eln 4 dx In e(x+1)

A: Given integral, ∫lnx2+x-lnx+eln4ln ex+1dx

Q: Demonstrate that for the integral of p(x)/q(x) where p(x) is of degree 2 and q(x) of degree 3 it is…

A:

Q: Find the linear approximation of f(x) = ln x at 1 and use it to estimate ln(1.33). L(x) In(1.33) =

A: Given : fx = lnx

Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: 17. Consider f(x) = dt. DO NOT state that f(x) = In x but explain how it behaves exactly like the…

A: In the question we need to evaluate the integral.

Q: The function g(x) = ln(x³ – 1) defined on V2, 0) is not zero unless x 2.

A: Given statement

Q: (B) Verify the Mean Value Theorem for f(x) = ln(4x + 1) on | 0,

A:

Q: 1. Evaluate the ff. integral f, (5x6 + 3x³ + 6)dx ·1

A:

Q: Let f(x) = x ln(1+ x*). For all æ € [-1, 1], it is known that In(1 + x) = (-1)" -xn+1 n +1 n=0 2.…

A: Substitute x3 for x in the given power series of ln1+x and simplify.…

Q: b) Is the Soluticn increasing or P N decreasia a when between o and te canyjug capacity

A:

Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

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Q: 6 1) Find the general antiderivative for f(x) = 1+ x?

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Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

A: Given that: ∫0∞ x2 -5e-3x dx To find: The value of the given integral. Let I = ∫0∞ (x2 -5)e-3x dx…

Q: Solve the initial value problems in Exercise for x as a functionof t.

A:

Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A: Concept: L'Hospital rule:Let f and  g be functions that are differentiable on an open interval (a,b)…

Q: Prove that coshz =log ztv= {Hint : cosh z =e} 2.

A: Use the hint and prove this.

Q: 1 Find the most general antiderivative of the function x3 + 4x

A:

Q: Differentiate the following

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Given f(x) = ln(ln æ³) Diberi f(x) = ln(In x³) %3D 3 Show that Tunjukkan 1 f' (x) = xlnx %3D

A: Given that the function is fx=lnlnx3 and it is required to show that f'x=1xlnx.

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: 2. Use the linear approximation of f(x) = x² ln(x + 1) to estimate (1.01)² ln(2.01).

A: We need to estimate value.

Q: If X is an exponential r.v. with parameter 5, identify the r.v. 10X

A: Introduction: The random variable X has an exponential probability distribution with parameter, λ =…

Q: 7. (4ea) Evaluate the definite integrals. a) L (3x2 + e*) dx

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

Q: 1. Let X be a lifetime (in hours) of a lightbulb and suppose that X has a PDF of (e0.001x f(x) = {…

A:

Q: Please see picture

A: Introduction:Here, MX (t) denotes the moment generating function (mgf) of the random variable X;…

Q: Show that -E{t, log(sigma(w*x)) + (1 – t;) log(1 – sigma(w"x;))} = E, log(1+ e-yw* x %3D Where…

A:

Q: 5. Express the integral: e- dr in terms of gamma function.

A:

Q: Let f(x) = 9 · 5" ln(5). Find the most general antiderivative. F(x)

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Q: Q7: Use the MEAN-VALUE-THEOREM to show that x-1<e* < 2x+1, 0<x<ln 2.

A: Since you have asked multiple question, we will solve the first question for you as per our…

Q: 9 3 Iff is continuous and f(x) dx 8, find f(x2)dx

A: Given as

Q: 1 dt, for x > 4. In(t) Let F(x) 4

A:

Q: 5- Suppose X, and X2 are i.id observations from the pdf fa,ß (x) = axa-1e-x" ,x>0, a > 0 Show that…

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Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A: Consider the limits:

Q: Determine the expression of the integrating function if it is known that: e) S; f(x)dx : - sen(9) +…

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Q: Show that the following functions all grow at the same rate using properties as x co: fi(x) = x°,…

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Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

A:

Q: h(x) = (5x-1 d) m(x) = (4x² – 9x} %3D

A: Product rule of differentiation: u·v' = u·v' + v·u'   ddxxn = n·xn-1 ddxf(x)n = n·f(x)n-1·f'(x)

Q: 5. Show that |Logz|<|In(z)|+ t, for all z # 0.

A:

Q: 9) Given the function f(x)=-3x+2 , find the net signed x-axis over the interval [-5,3]. area between…

A: Given function is  f(x)=-3x+2 We have to find the area of the region bounded by the given function…

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

A: