If g is a differentiable function and g(0)=0 and g'(0) > 0. a) Prove that f(x) = 1/2 (integral from 1 to x) (x-t)g(t)dt f is differentiable. b) f has a local minimum at x=0 by using the definition of f

Q: An RC circuit with a 100 Q resister and a 10^(-2) F capacitor is driven by a voltage…

A:

Q: 4. Let V : R? → R be a differentiable function. (i) Suppose r : R → R? satisfies the equation (t) =…

A: (i.) Given: A differentiable function, V:ℝ2→ℝ The function x:ℝ→ℝ2 satisfies the equation ddtxt=-∇Vxt…

Q: Consider the following function f: R -> R,whose criterion is f(z) = 43x' + 6x – 5 + e9(z) with g a…

A: If you like the solution then please give it a thumbs up.. The Answer is:        f''(a) = 258a + 81…

Q: t f(x+y)=f(x)+f(y) + 2xy-1 for all real x and y and f(x) be a differentiable function. [f f^ prime…

A:

Q: Determine, with justification, whether the series converges absolutely, converges conditionally, or…

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: Let ƒ : [a, b] → R be differentiable on [a, b]. Let λ = R be such that ƒ'(a) < \ < f'(b). (i) Let h…

A:

Q: 2. Use the theorem in Sec. 23 to show that f'(z) and its derivative f"(z) exist everywhere, and find…

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

Q: 3. Let f(z) be an analytic function in D = B₁(0) = {x² + y² < 1} and f(z)| = 1. Show that f(2)= C.…

A:

Q: Show that the functions f (x) = I x I and g(x) = x 1/3 are not differentiable at x = 0

A: Derivative of x at x=0:   Plotting: x,  xx

Q: 4. a) Find an approximation for f (x, y) = at the point (1.97,1.02). V10-r-5y b) Check Euler's…

A: (a) Approximate f(x,y)=410-x2-5y2 at the point (1.97,1.02) (b) Check Euler Theorem for…

Q: Consider the equation G (x + y + z) −F (x + y + 1) = 2021, which implicitly determines z as a…

A: Given equation is Gx+y+z-Fx+y+1=2021 Here, z is the function of x and y.

Q: L. Let h (x) = f (x) g (x). Find a. h' (1), b. h' (3), and с. h' (4).

A: According to the given information,

Q: anction of z = x + iy

A:

Q: Prove from the definition of differentiability that the function f : R\{3/2} → R f(x) = 3 – 2x is…

A:

Q: 26. Evaluate the gradint of f (x,y,₁z) = log (= ² + y² +₂²) at (1₁91)-11

A:

Q: Define f:c[-1, 1] → C as ƒ(x) = L₁x(1)dt – fx(1) di Find f.

A:

Q: 2. a) Give an example of a function f: R →R that is differentiable everywhere and 1- to-1, but f'(x)…

A: Let, f(x) = x3 .      Then, f(x), being a polynomial, is differentiable for all x ∈ R, i.e.,…

Q: Let (img) Use the fundamental calculus theorem to determine the slope of the tangent line to the…

A:

Q: Let z= x+iy and determine where the function f(z) = Log(z2 + 1) is holomorphic. What is its…

A: The derivative of f(z) is given by the chain…

Q: 2.Use the Fundamental Theorem of Calculus Part 1 to find the derivative of the functions 17 yt a)…

A:

Q: Let a differentiable function z = f(h²(x² + y3), 2łn(x +y)) satisfying the condition f(4,0) 1 be…

A: We need to find the partial derivative of z with respect to x for the given function.

Q: (3) Let f : R –→ R be a differentiable function everywhere. Prove that if f (x) = 0 has n solutions,…

A:

Q: Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx -…

A: f(x,t)=etlog(x) satisfies Black-Scholes equation: ft = f - xfx - x2fxx

Q: Example: Show that the function Az) = z² is analytic. z = x+iy S(2) = z

A:

Q: (Continuation of Exercise 31.) If ƒ is continuously differentiable on [0, a] for a > 0, and f(a) =…

A:

Q: A bounded, 3B > 0 such that |f(x)| < B Vx € (0, 1), continuous function on (0, 1) with unded…

A: We will find an example