t) := inf{a > 0 : wf(a)

Q: Let X ~ N (0, 1). Demonstrate that E (X)=0 and V (X)=1.

A: To demonstrate that E(X)=0 and V(X)=1 for a standard normal distribution X∼N(0,1), we need to…

Q: L{f(t – a)u(t – a)} = e¬as F(s) |

A: Topic:- Laplace transform and it's properties

Q: f (t) =1*b +acosh 21 + bsinh 21 a+b

A:

Q: Let f(x) = r e-t dt – 1/2. Find root to f(r) by using bisection method. You should find the interval…

A: As the given integral is improper and have no closed form solution; we will use numerical…

Q: Let f(r) = re. Find f'(r).

A: f(x)=xex2

Q: Suppose f(x, y, z)=x+y+z, h(x,y) = (x + y, x³, y) and g(x) = (x,x²). Calculate d =z=of oho g(x). dx

A:

Q: QO use best linear approximation to (F(Xiy) = ²³ to estimate the value of f at the point (0.0),…

A:

Q: Let F(x) = S c²dc. Compute F'(t) = F(t).

A: The fundamental theorem of Calculus says: If F(x)=∫0xf(t) dt...(1) then  F'(x)=dFdx=ddx∫0xf(t)…

Q: Consider the function f(x)=1/x+4. a) As x→−∞, f(x)→ b)As x→∞, f(x)→

A:

Q: Knowing fli) = 3, f (1) = 27. find d (7) at

A:

Q: Let F(t) = (4t³ - 1)j + (5t+2)k. Find F'(t). 7"(t) O 288t 288t³j 05+288t³ O 36t³ +5 O None of these

A:

Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

A:

Q: Find (r.)ifr=√.e and r₁=(. In (21)) r, dt

A:

Q: Find af if f(x, y) = xexy and x(t) = t² and y(t) = dt

A: Step 1:

Q: Evaluate (z – i) dz where C:y(t) = VE² +1 + it³, 0<t < 1

A: We have to find ∫Cz-idz where C: γt=t2+1+it3, 0≤t≤1

Q: Suppose f is a function for which f'and f" exist. You are given that: S(0) = 1 S'(0) = 5 %3D %3D…

A: here we use the integration by parts see below the answer and calculation

Q: hup lict funcrion F(xig) = x?y -eto =0 P(e, 1) Find y" (e) = ?

A: Here to use implicit diffrentiation method for solving the problem

Q: Let f(x) = sin? (x). Define F(x) | f(t) dt. What is F" -) ?

A:

Q: If f(t) = (12 + 7t + 5)(5t² + 4),

A: To  a.find f'(t) b. find f'(3)

Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

A:

Q: Let f(x, y) = 6e sin(7y) af af dy

A:

Q: If f(u) : f'(u) = V13 + w'dw then

A: Let,

Q: Given f(x, y) = 9xy® – 6x*y. Compute: a?f ду? ||

A:

Q: If f(x) is continuous on a, b] thenF(x) = So f(t)dt is continuous. OTrue False

A: We need to check whether the given statement is true or false

Q: Te dy 6. (18x y)", then is given by: 45 13 6. 4. (18x 13 45 13 6. (18x 13 45 6. (18x 45 6. (18x 13…

A: ⇒f(x,…