12. Given f(x) = x² – 4 and g(x) 2x 1, find [ f•g](3). - O A. 21 B. 14 O C. 9 O D. 5

Q: 13. If f(x) = 1 / (5 + 7x) , find S f(x) by using a u-substitution. Show the u-substitutions.

A: Given, fx = 15 +7x  We have to find ∫fx using u substitution

Q: 9. 3 If f is continuous and f (u) du = 3, then / (4xf(x²) + f(3x)) dx is equal to

A:

Q: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

A: We will solve this question by  differentiating f(x) and then finding the intervals for which the…

Q: 6. Suppose t > 0. Consider the functions f(x) = e* and g(x) = xt. Show that ext for all x > 0, if…

A:

Q: Given: mZ3 > mZ4 Prove: FÁ is not 1 to EG H. 4 E F

A: Note that the perpendicular lines intersect each other at an angle of 90°. Assume that FH→⊥EG→. Then…

Q: Suppose f(x) is the function such that for a > 0 we have f(x) = (e" – 1) In(x) and for x < 0 we have…

A:

Q: b) Suppose that f(x) = }Bx + 2 SBx² – 3 if x 2 Find the value of ß so that f(x) is continuous…

A: The given continuous function is,

Q: He)=(x+2)e f has absolute extreme values on ?

A:

Q: Consider the function f(x) = ax + b, where a and b are constants. Which of the following is one of…

A:

Q: 4. If fdx = f(x)[In(x) + 1] + C, then f(1) =

A: We have, ∫lnxx2dx = fxlnx+1+C To evaluate : The value of f1

Q: 5. Find the most general antiderivative of the following function. 2x² +5 f(x) = x² +1

A:

Q: Q2g If DF(x) = f(x+h)-f(x) for fixed h then find sh (ex-)) = ?

A: We have to find the △h(e2x-1).

Q: dx Evaluate: (x² + 4)² (2² + 4) tan¬1 (품) + z +C f (x) = 16 (a2 + 4) B None of the above © f (x) =…

A: Given integral is I=∫dxx2+42

Q: For what value of the constant c is the function f continuous on (-o, o)? { Cx2 2x if x < 5 - x3…

A: Observe that, f (x) has discontinuity at x = 5.If it is continuous at x = 5, then continuous on…

Q: For what value of the constant c is the function f continuous on ( - 0, 00) where cx + 6 if a 7

A: Given      fx = cx+6            if x≤7cx2-6          if x&gt;7To find      Value of c where function…

Q: Use the intermediate Value thereom to Show that gid=0 g(x)=0 on the interval E3,6] for quu)eメースメ-IS…

A: g(x)=x2-2x-15 on  [3,6]

Q: 2. Evaluate whether the following initial values is true in the function: y = 4cos-+ e-2x 2.a) 2.b)…

A: Given , y=4 cosx2+e-2x

Q: 3 Suppose S f(z) dz= 6 and S g(x) dz = 4. T3= -1 -1 Evaluate (-2 f (x) + 2 g (x)) dr. 1 Remember to…

A:

Q: For what value of the constant c is the function f continuous on (-0, 0) if x < 5 f(x) ={ cx? + 8x…

A:

Q: On what interval(s) is the function y = –2x² + 3x/3 both increasing and concave down?

A:

Q: 7. For what value of the constants A and B is the function f continuous on (-0o, 0)E AV-x+6-1 for x…

A:

Q: iii. Does there exist a function x e X such that 50) = f + [ e*: e x(s) ds x(1) = 1² for every t e…

A: It is given that X=C0,1 with the following norm, x=maxt∈0,1 xt The map T:X→X defined as follows:…

Q: For what value of the constant c the function f continuous on (-o, co)? S cx? + + 9x if x < 4 f(x) =…

A:

Q: 4. If f(z) is the principal branch of z3, find f'(–1– i).

A:

Q: 2. Supposethat f(x)=?βx? −3 if βx + 2 ifx≤2 x &gt; 2Find the value of β so that f(x) is continuous…

A:

Q: Please

A:

Q: For what value of the constant c is the .! function f continuous at x-3 |cx – 2 , if x 3 2 -1 -2 1

A: If function is continous then,limx→n+ fx =limx→n  fx = fnat point nso at given point x=3limx→3+ fx…

Q: Find the particular antiderivative F(x) of f(x)=4x−3 that satisfies F(1)=8.

A: The given function f(x)=4x-3, its antiderivative satisfies F(1)=8

Q: 1. Use the function f(x) = 4x°e* to answer the following problems: (a) On which interval(s) is the…

A: The given function is: fx=4x3 ex (a) To find the interval in which the function f(x) increasing?

Q: 3 B Consider the following function, z= x -2xyty't yn Lind the alues of ag Ddz,z,when redgyel dy 6.

A: Given : z = x2 -2xy + y3 + yw

Q: Suppose f(x, y) = 2 sin(11xy) and g(x, y, z) = v144 – x2 - - Find the following function values. f…

A: Suppose f(x, y) =2 sin(11xy) and g(x, y, z)=√(144 - x2 - y2 - z2) To find the following function…

Q: 2.Find an example different from the one in the text showing that (f ∗ 1)(t) need not be equal to…

A:

Q: For what value of the constant c is the function f continuous on (- o, 0) wh- cx + 7 if x 8 C =

A:

Q: 3. Given f(x)=-x+4x+12, 0sx58: (a) Carefully, graph S(x), 0Sx s8.

A:

Q: 2. Compute / f(x)dx for the following function. O if x 0 f(x)

A:

Q: Q1- If we have the following function: f(x, y) = 5 x8 y/3 + In x + e*y find fxx fyy f xy, and f yx…

A:

Q: Suppose F(x) is between 4 and 8 for x in [3,12]. What is the largest that · 12 L" F (x) dx can be?

A: given that function F(x) between 4 and 8 for x in [3, 12] we have to find the largest value of…

Q: 11 Suppose that f:R → R is a continuous function for which f(u) du=12 . | f(2x+3) da . Your answer…

A:

Q: 5 Suppose S f (x) dr = -8 and S g(x) dx=9. %3D -3 -3 | Evaluate S (2 f (x) + 4 g (x)) dr. -3…

A:

Q: 1/ Find the domain of the following functions : 1 1) f(x, y) = x²+y²+z²+16 2) f(x,y) = In(9 - x² –…

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Q: (b) If 38 10z f (2) = (2** + 6) e then at how many points the function f (z) is not differentiable?

A: f is every where differentiable, there are no points such that the function f(z) is not…

Q: 9 3 Iff is continuous and f(x) dx 8, find f(x2)dx

A: Given as

Q: O Caloulat 2nd hounene f(x)= sT こ>×ラ0 2. う2×23 With flx)> f(x+3n) Yne 忍

A:

Q: 38. At what value of x should the function f(x) = In(x – 4) approach to so that f(x) will be as…

A:

Q: H.w: Find LT-' of the following functions: 1- L-1 s2-2s+2]

A: Dear Bartleby student, according to our guidelines we can answer only three subparts, or first…

Q: of of and Find dy for the following function. f(x,y) 3 е 4xу In (6у) of of II

A: If the function is a multi-variable function then to find the derivative with respect to one…

Q: For what value of the constant b is the function f continuous on (- 0, ∞) where x2 – 36 if x 6 1 6…

A:

Q: 2. Find the principal part with respect to x for x 0 of the infinitesimal f(x) = = Vx + Vx. (That…

A: We have to use expansion of the function after some manipulations.

Q: Suppose that f: R→R is a differentiable function, satisfying f(3)=5 and f(x) dx=8. 3 /x-s'(x) dx?…

A: