Q.1) The integrating factor f(x), to solve ODE (x-2)y'-(x²-4)y=x-2, is: x² a) f(x)= -² b) f(x) = 2x e c) f(x) = ex d) f(x)= e

Q: Find the differential quotient of the following functions: a) f(x)=5x–2 b) f(x)=x2 +3 c)…

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Q: If f(x) = (5x +7)°, then the value of (f-1 (x))' at (f(-1),-1) is

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Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 f'(2) = g'(2) =…

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Q: Find a function f(x) such that f'(x) = − 5eª + 3x and ƒ(0) : = f(x) = - 1

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Q: Find the third derivative of f(x) = 3√x³-5cosx. 45 O f(x)= 4553 9 O f(x)= - O f(x)= 45 O f(x)= - 9…

A: It can be written as f(x)=3x3/4-5Cos(x)

Q: 13. f(x) = (x³ - Зx)(2x? + Зх + 5)

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

Q: Find a function f(2) such that f (x) = e + 7x and f(0) = - 1 f(x) =

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Q: Find g(1) if f (1) = 0, f'(1) = 2, and (fg)'(1) = 10.

A: The value of a function is obtained by substituting a value from its domain in the function…

Q: ren that f(x) = 6x - 6 and g(x) = 2- r', calcula f(g(0)) %3D 9(/(0)) - %3D

A: The question is taken from the above function and we have to find the composite function at the…

Q: If f(3) = 1, f'(3) = 1, g(3) = 1 and g' (3) = -2, then P dz g(x) I f(z) %3D Answer:

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Q: H (x) = VI-Soe? 2. %3D (f09) (><)= H (sc) %3D %3D 9(36) =

A: Given fgx=1-5x2

Q: Find a function f(x) such that f'(x)% = - 3a? + 8 and f(0) = 1 f(z) = %3D

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Q: F(x) = f(f(x)), G(x)= (F(x))2 f(6)=11, f(11)=2, f'(11)= 14, f'(6)=14 F'(6)= ? G'(6)=?

A: given: F(x)=f(f(x),  G(x)=(F(x))2 f(6)=11,f(11)=2,f'(11)=14,f'(6)=14

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(6) 7, f(7) = 2, f'(7) = 13, f'(6) = 6…

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Q: 1) Consider the functions ƒ(a) = 100 – 2¹ª and F(x) = f(t 1² f(t) dt. i. Write a simplified form of…

A: As per Bartleby guidelines we only give first question answers. Please repost for other parts.

Q: Suppose that f'(x) = 3x² + 3 – 1 and f(1) = 3. Find a formula for f(x) and then %3D %3D use this…

A: Topic- integration

Q: x² – 9 Let f (x) -. Find and simplify f' (x) and f"(x). %3D Ax2 + B f'(x) = where A = |-4 B = 54 C =…

A: Given that two function we find its first derivative and also second derivative and after find value…

Q: If x = e*-Y then is equal to A) B) log z (1+log z)* C)

A: solution:-xy=ex-ytake log both sideslnxy=lnex-yylnx=x-ydifferentiate both sides w.r.t…

Q: Find the second derivatives, f"(x) of O a) b) f(x) = 2x² + e²² F"(x) = 2e² (4x²+4) F"(x) = 4+e²²(x²…

A: dxndx=nxn-1dexdx=exd dx(a.b)=a.dbdx+b.dadxf(x)=2x2+ex2

Q: x) such that f"(x)=2r' +3x-4

A: Integration: f''(x)=2x3+3x2-4x+5; f0=2, f1=0 ∫xndx=xn+1n+1+c

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: f(x)=cos(x) Glx)こxや+1 d f(9(x) = t3 clx

A: We have to find derivative

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: Given that f"(x) and f(1) = 3x² + 2x – 1 and f'(1) = 0 3, find f(x).

A: Given equation is f ”(x) =3x2 + 2x -1 f ’(1) = 0 f (1) =3

Q: Use the values in the table below to answer each of the following: x f(x) g(x) f'(x) g'(x) f"(x) 0…

A: The table is given

Q: 4+ V4x glx) = 2 A) g'(x) = (x + 2)° + 2 B) g "lx) = **2 5 x + 2 %3D E) g (x) = 1- 2r D) g (x) = 2(x…

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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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