8. Iff₁=e¹x,f₂=e³x and fi,f2 and f3 are linearly dependent, the f3 could be (A) sin(3x) (B) ex (C) e 12x (D) ex-e4x (E) In (7x)

Q: Find the 1st derivative of the following. Differentiate implicitly. Simplify your final answer but…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Find derivatives of the following functions: y= (4x + 3)/In[2x* +3x -s] y= 3(e" +e*Xx² - 4)

A: ANSWER :

Q: 2 Find an x² x³ +3 anti-derivative for each of the following: for x³ +3>0 x + 2 x² + 4x² 5 a x² +1…

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Q: Given a piecewise function f(x) = 2, 2x² + 2x X log₂ (x-1), x < -2 -2 < x < 2, x‡0 x ≥ 2. 1. Sketch…

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Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: Find the derivative of the following function. y = In(6x² – 7x) – 4x А) 18х? -7х x(6х* - 7) В) 1 - 4…

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Q: Let f(x) = 3x + 1, x, = -1, x, = 0, x3 = 1, x4 = 2, and X5 = 3. Find E f(x,).

A: we have the given the following details   f(x)=3x+1x1=-1x2=0x3=1x4=2x5=3We have to find∑i=15f(xi)

Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Let 7 (t) = < - 2 cos(2t), Find F(t)dt (don't include the +C)

A: Please refer to the image below.

Q: s¯¹(x + 1) − √√14 − 3x², find ƒ¹(x). If f(x) = 3x cos

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Q: x3 C. g(x) : et

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Q: Determine which of the following pairs of functions are linearly independent. 1. f(t) = 3t, g(t) =…

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Q: Tx – 2VT+ V3 (2x2 – x) (3x - 2) - - Find D Do not use logarithmic differentiation.

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Q: 2. Find the anti-derivative of a. f(x) = 2x¹ - 5√√x³7−2e* ++ 3 1 1+x²

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: a. Suppose that ƒ(x) = g(x³) + eg(3x) where g' and g" exist. Find f' and f" in terms of g' and g".…

A: Here we have given a composition of a function as given below.

Q: Determine the inverse of Ax) = (x+2)² -3. j(x) =-2+x+3 b. (x)=-3±V+2 f(x) =-2+ x+3 d. (x)=-3+ +2 %3D…

A: The function is given by y = fx = x+22-3                                          ..........1 To…

Q: Compute the derivative of f(x) = (x² + 3)e7x+5. O (x² +2x+3)e7x+5 O 14xe7x+5 O (7x2 + 14x + 21) e7+5…

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Q: 2x 1) Calculate the derivative of h(x) = √√e²x +e-²x

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Q: 4. Examine if functions f(x)= x , f2 (x) = x², f;(x)=x² – 2x are linearly independent.

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Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

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Q: Determine which of the following pairs of functions are linearly independent. 1. f(x) = x² g(x) =…

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Q: 5. Find the inverse of f(x) = Vx+2.

A: f(x)=x+23To find: The inverse

Q: Suppose F′′(x)=Ax+B, with F′(1)=r and F(1)=s. Find F′(x) in terms of A, B, and r. F′(x)= Now find…

A: given  F''(x)=Ax+BF'(1)=r and  F(1)=sF'(x)=∫(Ax+B)dx∫xndx=xn+1n+1+c

Q: Let X1, X2, X3 and X4 be a random sample from population with pdf 0 < x < 1 X, fx(x) = 0, otherwise.…

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