Suppose that the functions q and r are defined as follows. q (x) =x²+7 r (x) = /x+8 Find the following. (e • r)(1) = 0 %3D (r • 9)(1) = D ?

Q: Find the general solution of the following Nonlinear first-order ODE. (Show the detail of your…

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Q: 3. Verify that the following functions are solution of one of the equations in part 1 and match the…

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Q: If f(x) In 2 + e9x find f '(0). f '(0) = | 9/2

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Q: Consider the function f(x) = -5x* – 11æ³ +x² + 2x – 17. What is the 3 smallest number n such that…

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Q: Q2) The critical points of the function F(x,y) = x + 3xy + y3 O (0,5) O (1,0) none of others O (1,1)…

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Q: Find a formula for f(") (x) if f(x) = e-10: fln)(z) =[]

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Q: Solve the following. If y= f(x) is a polynomial function of degree 3, then * f(x) dx

A: We have to find derivative

Q: This does not make alot of sense. If applying the definition how does the e^-st get moved outside as…

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Q: 29. If f(x) = Eo(k + 1)¿x* for x E (–1,1) then f"(0) = 12.

A: Here, we differentiate the given function and check whether it is true or false.

Q: 4.2 Apply the appropriate method to calculate the following: 1 = f***-8 I = S x2-4

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Q: Question #3 a) Find the x-position of all critical points for f(x)= 4x' – 15x² – 18x +1 (Show work,…

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Q: 11. Suppose that the equation g(x, y, z) = 0 determines z as a differ- entiable function of the…

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Q: 11. Suppose that the equation g(x, y, z) = 0 determines z as entiable function of the independent…

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Q: Find f'(x). f(x) = 3 In x+ Inx +2e* 7 3 O A. f(x)=-++2x e* x-1 6 X 3 B. f(x) =-+ 7 +2 ex 6 X Oc.…

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Q: 5. Suppose that f (x) dx = = 5, f (x) dx = -3, g(x) dx = -1, and g(x) dx = 2. Compute | (2f(2) –…

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Q: Find P(2 0

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: (1) Given functions are  f(x) = (2x2-1)(x2+3)x2+1  and g(x) = (x2+8)7(2-3x2)5

Q: Let X1, ·.. , X, " f (x;0) = e-=/°, x > 0. (i) Find the sCore and information functions of 0. (i)…

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Q: Find all critical points of the following function. 3. 3 f(x.y)=- + 8xy

A: To find critical points of f(x, y) we find ∂f∂x and ∂f∂y then equate to zero .f(x, y ) =…

Q: Determine the value(s) of x th your solutions and make a cc 1. f(x) = %3D x-1 2x-3 2. f(x) = x2-36…

A: A function Is discontinue at the point which is not in its domain

Q: If the pdf is K/1+x^2  0 < x < 2, Find K

A: To find K , from the probability density function: Given: Probability density function:

Q: The Gini index, given by 2∫10(x−f(x))dx2∫01(x−f(x))dx, is a measure of a country's income equality…

A: 2∫01(x-f(x))dx    , f(x) = x5.3

Q: If f(x) = e(n =)*) and g(x) = (In x)², then g(f (x)) is equal to.

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Q: Given f (x) = sin (z) and g (x) = x, the graph of the combined function h (x) = f (x) g (x) most…

A: Given  f(x) = sin(x) and g(x) = x

Q: Find a general formula for f^n. f(x)=7x^2 e^x

A: Consider the given function fx=7x2ex. In order to find the nth derivative f'n, differentiate the…

Q: f(x) = xsinx (-1)"x2n (2n+2)! .2n+2 OA. (-1)"r2n+2 (2n + 1)! O B. n=1 (-1)"x2n+1 (2n+ 1)! C. 1.…

A: Maclaurain series

Q: 1. If 2. If f(x) = 5x- 3x² – 2x + 7 f(x) = x* In x find f'(x) and f'(1). find f'(x) and S'(1).

A: Given:  1. fx=5x4-3x2-2x+72. fx=x4ln x

Q: 2х + A A. If dx = In [g(x)| + C then x2 + 4x + 5 A = and g(x) = 2х + B В. If dx = In |g(x)| – tan¬…

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Q: Question 2. Find the critical points of the function g(x, y) = x²y + 4xy.

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, currently…

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Q: Find a formula for f(n)(x) if f(x) = e' -3x fln)(x):

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Q: Find the x values of the two critical points of: 3(x- 1)23 6x – x² - 5 if x > 2. if x < 2 f(x)%3D X…

A: we have the given function is ;  f(x)=3(x-1)2/3if x≤26x-x2-5if x&gt;2

Q: If f(x) = x(e*+) , then f'(x) = %3D (A) (e + x³) x(e²+x²-1) (B) (e" + 5x*) In(x) æ(c*+z*) (C) (e* +…

A: To find f'(x) for the given function

Q: Suppose E(X) = 4 and E[X(X – 1)] = 25.5. (a) What is E(x2)? [Hint: First verify that E[X(X – 1)] =…

A: Given: EX=4EXX-1=25.5 So, a) EX2-X=25.5EX2-EX=25.5EX2=25.5+4=29.5

Q: If f (x) = x and g (x) = (x+ 3) (x – 1) (x – 4), find all x for whichf (x)

A: Given that, fx=x2gx=x+3x-1x-4

Q: If ɛ ER and the function f(x) = ex – 1+ x² is increasing x E R, show also that e >

A: Since f is increasing hence f'(x) &gt;0 for all x

Q: Calculate E(X³), where X has the following PMF: .5 x=1 f(x)=.3 x=2 2 x=3

A: Given that  PMF of X is  x 1 2 3 f( x ) 0.5 0.3 0.2

Q: 1) A course repeater claims that his brother who did some Calculus at college years ago, but…

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Q: S f(x) = x² – 2x + 6 x > 1 x4 + 2.x3 + 2 x <1 Show that there c E (-2,3) such that f(c) = 4. (Don't…

A: topic - continuity and limits

Q: Suppose that we don't have a formula for g(x) but we know that g(1) = -4 and g'(x) = V x2 + 15 for…

A: g(1)=-4, g'(x)=x2+15 Finding the value of g '(1) g '(1)=12+15=1+15=16=4

Q: (a): Find the value of k that makes function continuous at x = 4 %3D S 2x + 8 x > 4 x < 4 f(x) = 5x…

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

Q: If we use a linear approximation of e- at a = 0 to approximate e-1/3, then we obtain: А. 4/3. В. 2/3…

A: The solution is given below

Q: Find P(2 0

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Q: Find the critical points of the following function. e 3* + e f(x) = - 3x 2

A: The given function is

Q: 11) Internet rentals affect "k" Video in such a way that the demand for rentals of its DVDS changes…

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Q: Given that n2 1 and xn =V 4n² + 3n – 2n Will {Xn}, be divergent or convergent? n=1 Will E-1 Xn be…

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Q: 9. Find for each of the given functions using the chain rule. dx a. y = (4x + 3)3 b. y = v6 + x2 -…

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Q: Solve the following linear independent and Wronskian. 2. Are the functions y, = e* and y2 = x…

A: Here we have to determine whether the given functions are linearly independent.  We have,  y1=ex…