Find the solution of the initial value problem: y' (2x - 17)e, y(0) = In(72) = (a) Evaluate y(-1) (b) On what interval does this solution exist? The required interval is of the form (a, b). Enter the values of a and b (in that order) into the answer box below, separated with a comma. If either a or b is infinite, type either -infinity, or infinity for that value.

Q: Let h(x) = f(x)g(æ). If f(x) -3x? – 4x + 2 and g(x) = -x² + 3x +2, what is h' (-1)? Do not include…

A: Given, h(x) = f(x)g(x) f(x) = -3x2 - 4x +2 g(x) = -x2 +3x +2  We have to find h'(-1)

Q: Find an antiderivative F(x) of the function f(x) = 4x² - 6x +5 such that F(1) = 14. F(x)= (Hint:…

A: Solution is given below:

Q: The formula for a function y= f(x) and the graphs of f and f' are given. Find a formula for f-1 y=…

A: Given function is f(x)= x^7 +2

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Q: . For A= π/4 0 0 π/2 0 0 0 ㅠ calculate (a) A-2, (b) TI - A TI+A and (c) e¹A.

A: The given matrix A=π4000π2000π. We have to calculate the values of A-2, πI-AπI+A, eiA.

Q: Suppose = f(). (a) Given y(xo) = yo, when does this equation have a unique solution? (b) Make a…

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Q: f(x) = x²e²

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Q: Determine the solutions of the following first-order ODEs:  Tip:y'=xv'+v          y=xv *…

A: When a function fx,y can be expressed in the form of ϕyx or ϕxy, the function is referred to as…

Q: 5. lim (2x² – 5x + 1) x-1 A. 8 В. -8 C. -1 D. DNE

A: We can find the answer as below.

Q: (3)f(x) = x – [x]; 0x=5 (i) x=

A: Greatest integer function:  A function that results  in the greatest integer less than or equal to…

Q: The value of Jo(0) + Jn(x) + J_n(x) is O a. 1+ J,(x) [1+ (-1)"] O b. J„(x) [1+ (-1)") Ос. 1-2J, (х)…

A: From bessels function results

Q: Find a formula for f (z) if f(z) = I+1 f '(z) =O ( )'(2) =D-

A: We will use concept of inverse function and differentiation of a function.

Q: If n(Ax B) = 620 and n(B) = 31, find n(A). n(A)= n(B)= @)(::;:233)5

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Q: 1. If f(x) = ax² +b where a and bare real constants, then show that (a) f[xx] = a (x₁+x). (b)…

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Q: = (; ). -3 Find the general solutions of X' = AX with A = 1 -2

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Q: If h(x) = x - 1, then x is when h(x) = 1. а. 1 b. -1 -1 С. 2 d. 1

A: I think, there is some problem in question, so, don't worry I calculate both possibilities h(x) and…

Q: Given the function S 4x³ 4x3 – 18 x – 1 Calculate the following values: f( – 3) = f(3) = f( – 1) =

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Q: Solve In(x - 4) - In(x) = In 4 Select one: a. -2 O b. 2 c. 3 O d. 1

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Q: Solve the following ODE t y" – (1+t)y' + y = t² e' where one complementary solution is y1 = 1+t. %3D

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Q: The equation P (t) = 20 sin(2nt) + 98 models the blood pressure, P, where t represents time in…

A: Consider the function which models the blood pressure. P(t)=20sin(2πt)+98 Here P is the blood…

Q: Q1. Solve the Following. i) (367)9 + (715)9 = ( ?)9 ii) (715)8 - (367)8 = ( ?)8 iii) (296)12 +…

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

Q: Use the quotient rule to show the following: If n is a negative integer, and g(x) = x" then g' (x) =…

A: Solving by Quotient rule we can get

Q: If u(x) = x3, then du = 3x2.

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Q: If f(x)=2x-3, and g(x) is a function such that g"(0) = 4 and (fg)"(0) = -4, then g'(0) =

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Q: Consider the following functions. (x) = 2 + x, f,(x) = x, f;x) = x² g(x) = c,f,(x) + cof2(x) +…

A: A set of vectors {v1,v2,...,vk } is linearly independent if the vector equation x1v1+x2v2+···+xkvk…

Q: Find the values of the coefficients a, b and c so that the conditions f(0) = 1, f'(0) = -10, and…

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Q: The function h(x)=In(x² +c) is concave up on the interval (-4,4) and concave down on the intervals…

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Q: -Vx2+5 -x f(x): f'(0)? -x+2

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Q: Given and f'(-1) = Find f'(x) = -5 and f(-1) = 0. = and find f(1) = = f"(x) = 5x + 1

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Q: 20. '= 3 2 -1 2 1 -1, - (t) = -2t e² e³1 -4e¹-e-2t 2e3³t -e¹ -e-2t @3,

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Q: Given the functions f(x) = 3+ Vã, g(x) = x² – 3, h(x) 1 - x m(r): I - 3 find the following: 3x + 5'…

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Q: If f(x) = x + 2 and g(x) = x² – 9, find a formula for g(f(x)). O a) g(f(x)) — х + 2х — 9х — 18 - b)…

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