Evaluate the definite integral. i +e´j+tk )dt O e 7 – 1 e17 - (e-' – 1) + - (e~) - 1) j + k 17 O el7 – 1 17 (e" – 1) i – (e-l – 1) j + O el7 i - e-l j + 17 k | O el7 i+ (e-l – 1) j+ k 1 17

Q: if 2E2, f(2)= 12₁² find @if 20 then f/2) not exists Oif 2=0 then find f(z)

A: Given that fz=z2, then find  1) If z≠0, then f'z not exits. 2) If z=0,then find f'z.

Q: Let [*h(t)dt 2 She -8 -8 h(t)dt + [²h(t)dt =[ 3 I he -8 Use the given definite integrals above to…

A:

Q: A 3. Find (f g)(x) if f(x) = x2+x +1 and g(x) = x2 - x- 1. %3D %3D O (f 9)(x) = a4+ 2a + 3x? +2x +1…

A: We can find (f·g)(x) as below

Q: In Exercises 51–60, show that f(g(x)) = x and g(f(x)) = x. x – 1 51. F(x) = 2x + 1, g(x) %3D 53.…

A: 57. Consider the functions: fx=4x2-9……1gx=x+92……2 for x≥0.

Q: The domain off(x) = 3-x is 1-x2 %3D 1. R 2. R/{1,-1} 3. R/{3} 4. (0, ∞)

A: Domain: The domain of a function is the set of all input values for which the function is defined.…

Q: Evaluate the definite integral. e12' i + e¯*j+tk )dt e12 – 1 1 (e- – 1) + 12 O el2 – 1 e12 -i - (e-…

A: Integral

Q: Question 6 If E = 2ax + ay - 3az, F = ay - az, and G = 3ax + 5ay + 7az, determine (2E-3F)/|G| (A)…

A:

Q: 1²+z+3 Evaluate f dx (z-2)(z+1) Select one: O a. – In(x +1) +x+3ln(x – 2) +C O b. – In(x – 1) – x…

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Q: Evaluate the definite integral. ell! i + e¯'j + t k )dt O ell – 1 (e-1 – 1) - (ell – 1) i – (e-1 –…

A: The given integral is: I=∫01e11ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: 24. Differentiate each of the following with respect to x. Simplify fully when indicated 1 (a)_y=x²³…

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Q: 7х-1 dx х2—х-6 х-1 dr

A: As per our guidelines we are only supposed to solve first question in case of multiple questions

Q: The Wronskian of the functions e and e3x is (Select the correct answer.) O 2e1* 2x O 2e2* O - 2e4x O…

A: Given functions are: fx=ex  gx=e3x The Wronskian of the functions is given by: W=fxgxf'xg'x

Q: 5.Jf(x) =- 3x + 7 g(x) = 2x - 8 Find f(g(x))

A:

Q: Find the derivative. 4х — 3 y = 7x + 9 7(4г — 3) — 4(7а +9) (7ӕ + 9)2 4(7ӕ + 9) + 7(4 — 3) (7а + 9)?…

A: We have to find the derivative

Q: 12. Let y = f(x) be a polynomial function with derivative = x (x + 4) (x - 1)²(x − 3)³(x+2)4. On…

A: Given :- y=fx is a polynomial function ⇒dydx=xx+4x-12x-33x+24

Q: 1. d 3x²-5 dx 7x+1 3. 2. 7 sin(4x²)+e³ sechx² dx +4x² d³ dx³ -7x² + 4x-e³x

A: note :Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: 3. Evaluate the integral / Vr+3 (x- 1 4 4 (a) 극(z +3)72-(r + 3)52 + 국(2 +3)%2 +C 1 4 (b) (r + 3)"…

A: This question is related to Indefinite integration, we will solve it using given information.

Q: 3. Find (f g)(2) if f(x) = x² + a +1 and g(x) = x- x- 1. %3D %3D O (f 9)(x) = a* + 2 + 3x +2x +1 O…

A:

Q: . Let f(x) = ka. Determine the constant a so that f(-1) = 10 and f(2) = 5 19 4

A: Given query is to find the constants of the function.

Q: The graph of y = 8x - x² and the line y = 7 for 0 ≤ x ≤ 7 is shown. 18 16 14 12 10 8 6 4 2 0- -1…

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Q: %3D O 3. Find the first 3 iterates of the function f(x) = -2x+ 3 when xo = 0. O 1, 1, 1 O -2, 0, 2 O…

A: Iteration formula problem.....

Q: 2. 16X (x-6)(X+2) x +B

A:

Q: Enter each answer as a whole number (like -4, 0, or 253) or DNE for undefined ƒ(4) = lim f(x) = x→7+…

A: Note :  limx→a+fx means limit value of the function from right side to 'a' Note :  limx→a-fx means…

Q: Evaluate the definite integral. el8# i+ e*j+t k )dt O el8 i+ (e" – 1) j+ k el8 – 1 18 O el8 - e i+k…

A: The definite integral,      ∫01e18ti+e-tj+t kdt

Q: 2. y=(2x5-7)

A:

Q: xp²**** •1 х-1 2. '0 x²+3x+2

A: Given the definite integral I=∫01x−1x2+3x+2dx           ......(1)

Q: Use an appropriate substitution to integrate J 121*(+*+ 1)*dx .5 19 3x4 +c 3 B (x++1) 10 + c 10 u 10…

A: Option B is correct answer

Q: Evaluate the integral. | (5x² + 8) e-"dx -33e + 18 -33e-1 + 18 -33e-1 – 18 33e-1+ 18

A: Given, ∫015x2+8e-xdx  We have to evaluate the integral.

Q: 6.)f(x) =- 3x + 7 g(x) = 2x - 8 Find (gof)(x)

A: Since you mention that : answer for number 6

Q: Evaluate the defınite integral. 8 i + e¯´j+tk)dt 0, – (e-1 – 1) j+ k i-e'j+;k 8 (e* – 1) i – (e- –…

A: The given integral is: I=∫01e8ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: Help EVALUATE THE INTEGRAL

A: Step 1:  Step 2: Step 3: Step 4: