1.12 Student's t-distribution 8(0) = (1+²) (1+²) [√UB (12-2)]; f(t) with B(a,b) Γ(α)Γ(β) r(a+ß)' -00 < t < 00 Derive E(T) = 0 and var(T) = V v-2

Q: The derivative of requires the product rule and is given by Factor the derivative of f. g'(v) = g(v)…

A: Given:Here we have given a function  .To find:The derivative of the given function using product…

Q: 1 •[₁ F(X) -1 Given f(x) dx = 0 and (a) [f f(x) and [₁ f(x) dx. 1 (c) [₁² (d) (b) • [² f(x) dx - [°…

A: (a)

Q: { 1/(x + 2) , x2 , sin(x – 1)/(x - 1) , x 1. y = F(x) =

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Q: Find the equation of the line tangent to the graph of the indicated composite function at the…

A: Since there are multiple questions posted, we will answer the first question 13. Ir you want the…

Q: Find the derivatives of the following multivariate functions. Justify your answers. (a) f(x) =…

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Q: If f(x) = √√2x + 5, find ƒ'(x) using Chain Rule ƒ'(x)= Find f'(5). ƒ'(5)=

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Q: f(x) = In(2x) %3D (x), %3D

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Q: 9- 5+ 8 4 h(x) 7 6. 3 4 3 2 1 g(x) 1 3 x-values 4 1 4 3 x-values 1 9(x) If f(x) = then h(æ)' f'(3) =…

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Q: 5x2 If f(x) = 3 then f'(0) is 4x + 2 O 1/3 3 O - 3 O - 1/3

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Q: 2 Find f such that f'(x) = f(9) = 20. f(x) =O

A: Topic - integration

Q: 1. If the graph of y = f(x) contains the point (0,2), and f(x) > 0 for all x, then f(x) = dx (a)…

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Q: 8. A table of values for (x), g(x),f'(x), and g'(x) has been given. Make sure you show ALL…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: suppose that alpha(t) = 12t^2-6,with v(0) = 5 and s(0) = 10 find s(t) and graph alpha(t), v(t) and…

A: Given that, the acceleration function is at=12t2-6 and the initial conditions are v0=5 and s0=10,…

Q: 0.6z Express the function h(x) = Ve' - 3 in the form h(x) = (ƒ o g)(x) where f(x) # x and g(x) ± x…

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Q: 4.2 2

A: Differentiate the following:   F(x)=(6x+1)2

Q: (11) (g(h(x))) and h(1) = 5, g(5) = 3, h' (1) = 4, g' (5) = 10 and f'(3) = 8, then r' (1) = If r(x)…

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Q: (2, 1) Graph of f The derivative of a function fis defined by f'(x) =/1-2 in (2-), -5≤x≤2 where the…

A: Since you posted multiple question, we will solve first question for you. Kindly repost other…

Q: [UCONN 1071Q] Let f(x) = (e+ln(x2)). Which of the following represents the first derivative f'(r)?…

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Q: - 5 Let f(x) = – 5x Va + - f'(x) =

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Q: f(x) = In (x² + 1) %3D Note: 2x and f"(x) = 2(1 – x)(1+ x) (x² + 1)² f'(x) %3D %3D x2 + 1 (a) Find…

A: Here, we are going to solve the first two subparts and for the remaining subpart please post the…

Q: 11 Find /(x) if ƒ (1) = and the tangent line at (x, f (x)) has the slope 1 1xe*²-1 1 Oa. O b. 1le*-1…

A: Using formula of slope of tangent &amp; integration to find f(x)

Q: Let f and g be two differentiable functions. Suppose we know that f(2)=5, f'(2)=-2, f(1)=–3,…

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Q: For the following exercises, assume that f(x) and g(x) are both differentiable functions for all x.…

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Q: Use the quotient rule to find the derivative of 4x² + 2 k(x) 6x - 2 =

A: We know that the quotient rules of the d/dx(u/v)=(v*du/dx-u*dv/dx)/v^2

Q: Find the Maclaurin's polynomial of degree 3 for ( a) f(x)=(1+x)e²*

A: Maclaurin Series of f(x) of Degree 3 is : f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: Question 2 Using the graphs of f (x)and g(x) from the video, find k'(6), where k (x) = k'(6)= k(6)…

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Q: 3 If f(t)=e3t = f'(t) = 3-s

A: we have ft=e3t we know that  Lft=Fs=∫0∞e-stftdtLf't=sFs-f0So, Le3t=1s-3=Fs

Q: 8 x + 6 Let f(x) = x + 1 f'(x) =

A: The function is fx=x+6x+18. Find the derivative of the function using the chain rule and quotient…

Q: 7x Let f (x) : Then the derivative of f is %3D 1 + 5* f'(x) = A(1 + 5*) – Bx(5*) In C, where (1 +…

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Q: (10) For this problem let f(x) denote the fraction of total income earned by the lowest x fraction…

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Q: 3 Let f(x) : 4x + 6

A: f(x)=34x+6=3(4x+6)-1 ddxxn=n xn-1

Q: Find f such that f'(x)= 7x +7x-2 and f(0)= 8.

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