24 8. (10) Let g(x) = sin (x) if a +0 %3D 0. if r=0 Is g' is continuous at 0?

Q: Let f : R → R be a one-to-one differentiable function where f(0) = 8, f'(0) = -2, f(6) = 9, and…

A: Given, f:ℝ→ℝ be a one to one differential function. f0=8,f'0=-2,f6=9,f'6=8

Q: derivative

A: We will find the derivative.

Q: the line 3x+ y=l is the tangent line for the graph of y= f(x) at x=1, then f'(1)= 1 (C) 1 (D) 3 A) 3…

A: The slope of the line y=mx+c is m. The slope is equal to the derivative of y i.e., f'y=m

Q: Let h be a differentiable function with a tangent line at x = TT. The equation of the tangent line…

A: We have to find the value of h(x) at x=0,π

Q: 23. The graph of a differentiable function ƒ is shown. If h(x) = f(t) dt, which of the following is…

A:

Q: Prove tht the fallowing ralt U(1-k)-2U(t) + U(t + k) U" (t) =- with an enor of ortler k?, which is…

A: The objective is to prove the central difference approximation to the second derivative of Ut…

Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

A: Consider the given statement "If f is a continuous at x = c, then f has a derivative at x = c".

Q: (a) Let f be a function that is continuous everywhere and let F(x) = {(f(x) sin^2(x))/x  , if x ≠0…

A: We need to apply formula of derivative

Q: (20p) Let f be a differentiable function satisfying the equation f(a + b) = f(a) + f(b) + 2ab for…

A:

Q: Show that f'(z) and its derivative f"(z) exist in C when f(2)=e-¹e-iy

A:

Q: 2/5x-1=3/10x+7

A:

Q: The derivative of f(t) = 21° · h(t), where fand h are differentiable functions is: A. 10° · h(t) +…

A:

Q: 1. f(r +h)-f(r) Using f'(r) = lim %3D Find the derivative of f(r) = V3x- 4. %3D

A: To find the derivative of f(x)

Q: Use the graph of the derivative f' of a continuous function f is shown. (Assume f' continues to ∞.)…

A: Use the graph of the derivative f'(x) of a continuous function f is shown .

Q: The product of two numbers x and x + 170 can be simplified to be x + х.

A:

Q: 4x Let f (x) Then the derivative of f is %3D 1 + 4* f'(x) = A(1 + 4*) – Bx(4*) In C where (1 + 4*)D…

A:

Q: d Jcose d cose 'cos(r sin 0)]= [e* Telcom sin(tsin 0)]. (i) Show that t. %3D dt

A: (b) (i) show that t·ddtet cosθ cost sinθ=ddθet cosθ sint sinθ consider left hand side  t·ddtet cosθ…

Q: a) Find implicitly, if y°cosy +x = 2xy b) Define differentials also find derivative by using…

A: (2)(a) We have the given function as y2cosy+x2=2xy On using implicit differentiation, we get the…

Q: 3. Express the derivative of f (x) = Vx as a limit of the difference quotient ("h → 0")

A:

Q: 9 f:(-0,0) U (0, ∞) → (∞,0) U (0, ∞0). Where f(x) х Show that f(x) is continuous at x=3 with the…

A:

Q: 1. What is true about the function f(x) = b* ? (Circle ALL that apply) c. f'(0) = Inb b + 1 b. x>0…

A: Find your answer below

Q: 3. (a) Let f be differentiable on an open interval I and suppose f"(x) = 0 for every x in 1. Show…

A: Let f be a differentiable on an open interval I i.e. (a,b), Suppose that f'(x)=0 for every x in…