3. For a, b>0 define f(x) by f(x) = Tot tz ta dt log blog a Prove or disprove that f is continuous at x = -1. x = -1 x = -1.

Q: (v) Let f(x) = /2x – 1, for r > 0. Use the definition of the derivative to compute f'(x).

A:

Q: 3) Differentiation D: F[t] ---> F[t], is linear and satisfies Dt¹ = nt¹-1. It satisfies the usual…

A: (a) We have f(c) = 0 if and only if (t-c) divides f in F[t]. Thus, we can write f(t) = (t-c)g(t) for…

Q: Is f(x)= Vx + 1 continuous at x == -1

A: Draw the graph and check continuty with help of limit of function.

Q: Below is the graph of f'(x) (the derivative of f(x)). Assume that f(x) is continuous for every real…

A: Consider the given graph: f'2=f4−f04−00=f4−104f4=10

Q: 2. Let f be defined by { x 0. f(x):= I 0 Using the definition of the derivative, verify if f has a…

A: We need to find derivative.

Q: HiHtar is THe secoyd derivative OF Y

A:

Q: Find the weak derivative of f(x) = |x² − x + 1/5 on the - 1) interval (0,1).

A: 1.Given: fx=x2-x+15.To Find: The weak derivative of the given function on the interval 0, 1. Note-…

Q: et f(x) x8(x-4)³ (x²+3)8 Use logarithmic differentiation to determine the derivative. ƒ'(x) =

A:

Q: Suppose F(x) is a differentiable function for all real numbers x. Evaluate the following derivative.…

A: We need to find the derivative of the function F(x^4) with respect to x.

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Let f(x) = 2^x and g(x) = cos(x). Over what intervals is f(g(x)), x ≥ 0 decreasing? Show your work…

A: Let  and . Over what intervals is ,  decreasing?Show your work or explain your reasoning.

Q: Exercise 1. For the function f(x) whose graph is given below, sketch two functions F(x) whose…

A:

Q: 1 Let f(x) = 8 + In (t) dt, for x2 1. Find f'(2).

A:

Q: 1. Let f(x)=√x-2 / x-4 . Show that f(x) has a removablediscotuiti t x=4   2. Given f(x)= √(x+1).…

A: Here we have to find the derivative of a function at a point.

Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

Q: If I have a continuous, smooth (no sharp points) function with 3 local maxima and 2 local minima,…

A: Since the function is continuous , with 3 local maxima and 2 local minima.the function will have 5…

Q: Let f be the function with derivative defined by f'(x) = cos(x²) on the interval -2 < x <2. How many…

A:

Q: 1. Sketch a function f(x) with the following properties: f'(x) > 0 and f"(x) = 0, for r 2 . .

A:

Q: y 4 y = f'(x) 4. 2. 2.

A: Here domain of the function is not clear that causing confusion.

Q: If f has a derivative at x = 2, then f is continuous at x = = 2. True False

A: