Given the following differentiation rules The function (x) is continuous and differentiable and not the func A ]" = nc«)]x/(x) for every real number n B (k x /x)] = k x 4) for k constant

Q: Verify that the three conditions of the hypothesis of Rolle's Theorem hold for the function f (x) =…

A: 1. f(x) is continuous on the closed interval [a,b] 2. f(x) is differentiable on the open interval…

Q: A parallelogram is formed by the vectors [1, 2] and [3, -4]. Find the area of the parallelogram. O…

A: Given query is to find the area of parallelogram.

Q: Show that f-(A U B) = f-'(A) U f-'(B) and f-1(A n B) = f-'(A) nf-'(B) for any function f. Is the…

A:

Q: Examine whether the following function is Analytic or not ¹() (z) = ln(x² + y²) + i tan-¹

A:

Q: Are these functions injective or surjective?  f : R → R; f(x) = x^2,  f : R → Z; f(x) = bxc,  f :…

A:

Q: Prove that the following function is continuous on the interval [-5,5]: H(x)= the square root of…

A: Given, H(x)=25-x2we have to prove that the given function is continous on the interval[-5,5]…

Q: is there an easy way to determine what function, on a graph is f, f' , and f''

A: I have given an answer in step 2.

Q: 5. Ôx (@) = ¢x (- w), if X is symmetric function.

A:

Q: Please

A: For concave downward, f''(x) < 0 f(x) = (1-1/x)2 = 1 - 2/x + 1/x2 f'(x) =2/x2 - 2/x3 f''(x) =…

Q: Show that the GHASH function calculates (X1 • H™) Ð (X, · H"-1) © O (Xm-1° H²) O (Xm· H) ...

A:

Q: x -1 f (x): x² +3x %3D

A: If two functions f,g are continuous then the function f+g,f-g,fg are also continuous. The function…

Q: Let the function f:R-->R be twice differentiable and suppose that f(x)≤0 and f''(x)≥0 for all x.…

A: It is given that, the function f:R-->R be twice differentiable and suppose that f(x)≤0 and…

Q: (2n)! a"(n!)2 A) diverges if |a| 2² n-1 C) converges if |a| > 2ª

A: Here we have to find the converges or diverges of the given series.

Q: Suppose that the average number of M= (32+27t)/(2t+7) where t is the number of days on the (a) Is…

A: Given that: M=32+27t2t+7 Simplify it. M=27t+322t+7=272-1252t+7

Q: -3 -2 -i O Graph of f' The graph of f', the derivative of the function f, is shown above. On which…

A: We know that, Let f ' be the first derivative of function f that is differentiable on a given…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.