2x +1 (3x – 1) (a2 + 2x + 2) Evaluate: -da J A F(x) 2 In (|3x - 1|) + In (a2 + 2x + 2) – 4 arctan (x + 1) +C 10 2 ln (|3x – 1) - In (a2 + 2x + 2) + 4 arctan (x + 1) + C B F (x) = 10 F (x) = 2 In (|3.x – 1|) + In (x + 2x + 2) +4 arctan (a+ 1) +C 10 (D F (x) : 2 In (|3x – 1|) – In (a2 + 2x+ 2) – 4 arctan (a +1) +C 10 E None of the given choices

Q: Let f (x) = Evaluate the following. Simplify if possible. 9x +7 f (x) – f(a) a) 7 where A = A' for x…

A:

Q: S Sifoo-gool dx O d2 (f.g) = Sup {/fox) - gox|} V£₁9 € [0₂4] if d, (fig) = Find Ⓒd₁ (√x,x) @d₂…

A:

Q: x+3 4) Evaluate f dx x+1

A:

Q: 8 Use definition L{f(t)} = - S% e- 0 -st f(t) dt to find L{3t}

A: From definition of Laplace integral  for function ,, Here

Q: Show that an = 1/2n + 1 is decreasing.

A: Given: an=12n+1 Substitute 1 for n in the equation an=12n+1. a1=12(1)+1=13=0.333

Q: Compute divF and curlF for F = -r°(y – 2)i – (2² + y^)j+()k. 422

A:

Q: Let f(z) - 4z-1 pnd alz) - ar+b, where a pnd b are positive constants. If the composite

A:

Q: Calculate R3 and L3 for f(x) = x2-8x+2 over [1,4] .

A:

Q: The domain of the function f(x)=√12+4x−x^2 is the closed interval [A,B] where A= and B=

A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: Find an analystic function whose real part is e-x (x sin y-y cos y)

A:

Q: 6. (x – 1

A:

Q: 3 7) Evaluate: f(-x² + 4x − 1)dx 1

A: Given, ∫13(-x2+4x-1)dx

Q: Find the differentiate

A:

Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + sinx c) f(x) =

A: Differentiate wrt x

Q: [22] Express the function as a product by factoring the right-hand side: f(x)= x' +x² – 4.x - 4.

A: We have to express the given function as a product by factoring the right hand side: fx=x3+x2-4x-4…

Q: Let a, b 0. Find f(100) (a) provided that x³ (a - bx)²* f(x) =

A:

Q: x(t-1) * 6[t+1] equals x(t+a) where a equals. Answer:

A: Given, x(t-1)* del(t+1) = x(t +a)

Q: Differentiate the following function. 6x2 +5 y= x2 +1

A:

Q: る(4xナx)(10x2+x2-2

A:

Q: For the function f(z) 2(x – 5) + 7, which of these equations describes f '(r), the inverse of the…

A: We wil use concept of inverse function to find the answer.

Q: Q3 Find f-(x) for the following : 1- y = Jx-3 2- y = (2x³ + 1)'/5

A: For finding the inverse, we will replace x with y and y with x

Q: 2 Evaluate: ²₁²(x²-y²² du dt

A:

Q: π Show x² x² + x² +1 4 √3 -∞0 4 Hint: x² + x² +1= (xª + 2x² +1) − x² = (x² +1)² −x² dx =

A: The objective is to show that ∫-∞∞ x2x4+x2+1dx=π3

Q: Find 4 of 3xy –- x³ = 5 at (1, 2)

A: Given; 3xy-x3=5 at (1,2)

Q: differentiate f(x) = O O O O - 1 1 9x2+ 13x-5 18x + 13 (9x²+ 13x - 5) 3/2 1 (9x² + 13x - 5) 3/2 18x…

A:

Q: 2. Given that f is a differentiable function with f'(3) = -5, find g'(1) where g(x) = f(4x-x²)

A: The given function is,

Q: 5 Evaluate [ (x + 2)(x² - 1) dx

A: Solution:Given   let      I=∫25(x+2)(x2-1)dxFormula:∫xndx=xn+1n+1+C