(a) An antiderivative of f(x) = 5“ is 5 (i) F(x) = 5" +C (ii) F(x) = 5ª In 5 +C (iii) F(x) = : +C (iv) F(x) = :+C In r In 5 (b) What does the I in 'LIATE' stand for when using Integration by Parts? (i) I don't know (ii) Inverse Trig Functions (iii) Indeterminate Forms (iv) Irrational Numbers dr (c) The appropriate choice for r in Trigonometric Substitution for is + 4 (i) x = 2 sec 0 (ii) r = 4 tan 0 (iii) æ = 2 sin 0 (iv) a = 2 tan 0

Q: 3. Consider f (x, y) = a +6V-10. Compute the following: (a) (b)

A: Given,          fx,y=x4+6y-10

Q: If f(x) = f'(x) = 1 x³ 3 √t² + 1 dt then F

A: Here we will use the Leibniz theorem to  find the derivative of the given problem, so on using this…

Q: What is tl

A: Given function is: f(x) = 3 + cos (3x) We have to find the gradient of the function.

Q: If f(x) = 1+/x, then f'(x) = -1 A 4/xV1+/x 1 B 4V1+x 1 4/x/1+Jx 1

A:

Q: If F(x)=sinx+6x2−4 is an antiderivative of f(x) then f(x)=

A: If F(x) is antiderivative of f(x) , then f(x) is derivative of F(x) .

Q: If f(2) = 1, f'(2) = 2, g(2) = 2 and g' (2) = 1, then f(x) g(z) %3D %3D %3D

A: Given : f2=1f'2=2g2=2g'2=1

Q: If f(x,y)=xe/2+118x?y, then asf at (1,1) is equal to əx²əy³

A: Given function is: f(x,y)=xey22+118x2y3 Derivative of function with respect to 'x'…

Q: -1² ƒ'(x) = 3x² √√x6 +1 If f(x) = √t² + 1 dt then

A:

Q: f'(x) = f'(4) - L

A:

Q: Let h(x)=f(x)/g(x). If f(x)=−cos(x) and g(x)=4x^2+2x−3, what is h′(x)?

A: Given,          hx=fxgx. And fx=-cosx  and  gx=4x2+2x-3.

Q: Use Simpson's 1/3 rule to integrate f(x) = from a = 0 to b = 0.8. 0.2+25x200x²+675x³-900x4+400x-5

A: Using one time Simpsons 1/3rd rule.

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: If f(x) = x(e*+=') , then f'(x) = %3D %3D (A) (e² + æ³) æ(e*+z*-1) (B) (e" + 5æª) In(x) æ(e*+a*) (C)…

A: We have to find derivative of f(x).

Q: 8. Find f'(x) for (a) f(x)=(x² +3x+1)(2x+3) 2x-3x+1 (b) ƒ(x)= %3D

A: We need to find the derivative of the given functions. For (a),

Q: GivenF(x) = h(f(g(x))), g(1) = 2, g′(1) = 3, f(2) = 4, h'(4) = 1 and f'(2) = 6, findF′(1)

A:

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: Find the Maclaurin's polynomial of degree 3 for ( a) f(x)=(1+x)e²*

A: Maclaurin Series of f(x) of Degree 3 is : f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: Given f(x, y) = e(lnx) + ln(xy) - 8x² find f(1,e)

A:

Q: uestion hat is y' (x) when y(x) = (4x³ + 6x)*?

A: * Logarithmic function property : ln ( an ) = n ln ( a ) * Product rule of derivative : ( f • g )…

Q: Let h(x) f(x) where f(x) = In(3x2 + 2x + 2) and g(x) = -2x. What is h' (x)? g(x)' Select the correct…

A:

Q: 1 Suppose f(x) = v2x + 4 and g(x) %3D 2x + 5' (f o g)(x) (go f)(x)

A: We have to find function

Q: Evaluate f"(c) at the point. 9) f(x) = In (4x - 3), c = 1 10) f(x)=3x2-3, c=1 3x - 4 11) f(x)= 4x-3'…

A:

Q: If f(x) + x°(f(x))² =34 and f(1) = 2, then f'(1) = %3D %3D

A:

Q: f(3) = 5, g(3) = -4, f'(3) = -2, g'(3) = 7, f'(5) = 3, g'(5) = 10 a) If h(x) = f(x)g(x), find h'(3).…

A: topic - functions and derivatives

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'…

A:

Q: True or False if f'(x) = i +t2j and f(0) = j - k then  f(x) = ti + (t3/3+1)j

A:

Q: Let F(x) be an antiderivative of f(x), with F(1) = 20 and * f (x)dx = -7. What is F(4)?

A: