Let o € C (RN), heR - {0}. For teR', we set 0(r +th) – 6(x) (1) = t. 1- Show that o e C (R^).

Q: 13. If f(x) = 1 / (5 + 7x) , find S f(x) by using a u-substitution. Show the u-substitutions.

A: Given, fx = 15 +7x  We have to find ∫fx using u substitution

Q: x if x20 If Ax) = -x2 then f'(0) if x <0

A: Given function, fx=x2      if x≥0-x2   if x&lt;0

Q: Suppose that f(x) Evaluate each of the following: f'(3) = %3D f'(-1) =

A: Given function is : fx=3x9 The given function can be written as : fx=3x-9

Q: 5) — = [(-D)" (2-1)", when 12-1}<1. n=0

A: Introduction: A geometric series is a type of series which is in the form as follows:…

Q: Let f(x) = 6 + V4x – 5. Find f-'(x). f- (x) = for x > 6

A: Given f(x)=6+4x-5 The objective is to find f-1(x).

Q: Find Cn in terms of C0 when: 1. Cn = Cn-1/(3n2 + 4n): (Note that C1 = C0/7, C2 = C0/140, C3 =…

A:

Q: Let f(x) = 1. f'(2)= 2. f'(5)= 3 √x Evaluate each of the following: A

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Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

A:

Q: Let f(t) = 3t – 8t + 5e'. - Then f'(t) =

A:

Q: Let 7(t) = Find (t) 7' (t) =

A: Given query is to find the derivau of r(t).

Q: 11. Given /(r)-V1-2, fnd onctions /and g so that. /(r) (/o9)(r).

A: Here, we must express H(x) as a composition of two functions. This can be done in multiple ways. One…

Q: Let F(t) = (4t³ - 1)j + (5t+2)k. Find F'(t). 7"(t) O 288t 288t³j 05+288t³ O 36t³ +5 O None of these

A:

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Suppose X,~ Uniform(0, 2) and X, ~ Uniform(0, X,). Find E[2X,+X,].

A: Given,X1 ~U(0,2)X2 ~U(0,X1)E(X1)=2+02=1E(X2)=X1+02=X12

Q: -2 Suppose f(x) = f(x) dx Evaluate: A - In (2) B - 4 3 16 D In (2)

A: Solution... Answer is.  Option..(B)

Q: a) x³ - x f (x) = 2x² + x − 1 - b) f(x) = ax + b cx - d

A: Here we have to evaluate for a) and b) the value of f'(x).

Q: Example 4. Differentiate with respect to 'x': 2 - 3x + 4 - X + x + 2

A:

Q: Let f(x)=x²- 3 g(x)=Vx+7. Find f(g(2)) 8 О 12 О -12 O O O O

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Q: 1) If f(x) = x²(2), find f'(2)

A: f(x)=x2∫2xdtt2+5we know  d dx(∫axf(t)dt)=f(x)×d dx(x)-f(a)×d dx(a)

Q: Show that Var (Y) = Var(ε₁) = 0².

A: Let us consider a simple linear regression. The equation of a simple linear regression model is:…

Q: If X~BET(1,2) then E(X)= (1 2/B (1/B

A:

Q: Suppose f(x) = 6t²√1+tº dt. 1) Evaluate f (2). 2) Evaluate f'(2). 3) Evaluate f"(2).

A:

Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

Q: Let fCx) 10 t 7x what is f'(×) ?

A: Given function is as below:

Q: Let X ~ T(a, B). If E(X) = aß and E(X²) = aß² + a² ß². If â = X, find the method of B moments…

A:

Q: 7. Ax)= 2x' -5

A: We have to find

Q: Let f(x) = x³ + √√. Then f'(1) = 02 O 1.5 O 3.5 04

A:

Q: Let f(x)= x³+1. Then (fof)'(1)= O 20 O 36 O 3 O 9

A: Please refer to the image below

Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

A:

Q: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

Q: Suppose X and Y are independent variables such that E[X] = 2, E[Y] = 3, E[X^2] = 9 and E[Y^2] = 15.…

A:

Q: Find the arc length (s) of the curve 7(t) = (e*, 4e", - 2et) for 0 <t < In(5) |

A: we are given the curve  r→(t)=e5t,-4e5t,-2e5t =e5ti-4e5tj-2e5tkwhere 0≤t≤ln5

Q: y 5 4 f(x) 3 g(x) 2 2 3 4 -1 1. 1.

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Q: z2+5z+6 "f(2) = and C: z=3, then f (z)dz =? %3D3• N-2 O a. 0 O b. #0 Oc f(z) is not analytic O d.…

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Q: 2 – 22 If f(x) find: 5 + x2 f'(x) = %3D

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Q: Determine the value of 'k' if the L[ tk4t ] = 1/(s² - bs + 10).

A:

Q: Compute Projs w given by W = [2 -1 -2] and S is defined by x = s [2 − 1 2] + t [−1 −13], s, tER.

A: