a) Is the function f(x) = x+ odd, even or neither

Q: В. B. Show that the function f (z) = -i z2 is analytic.

A: The solution is given as

Q: Describe the long run behavior of f(x) - 2? As x → - 0o, f(x) → ? As x → 0, f(x) → ?

A:

Q: Consider the function f(x) = xn , where n is odd. Does f −1 exist? Explain.

A:

Q: Find the domain of f(x) = 1/x and discuss the behavior of f near any excluded x-values.

A:

Q: If f"(x)>0 on an interval I then...

A:

Q: Verify Rolle's theorem for the function f(x) = 2x2 – 20x + 33 on the interval [2, 8]. -

A:

Q: 10 The function f(x) = - has a removable discontinuity at x = 2. To remove the - 2 discontinuity,…

A: Given: f(x)=10x+x2−4x−2

Q: Is the following function continuous? [x² + y² _if x² + y² ! f (x, y) =

A: The left-side limit, the right-side limit, and the value of the function at that point can be…

Q: 4х+7 (ii) If f(x)={ 1<x<2 determine whether the function f(x) is continuous 14x² -1 2<x<4 throughout…

A: Continuity of the function

Q: The function f(z) is analytic if

A: analytic functions are functions which are locally given by the convergent power series. i.e any…

Q: 2. Determine whether the function y= -x5 + x3 – 1 is even, odd, or neither. Justify your ans wer.

A:

Q: Let f(x) = x^2 −x −2. Using the Intermediate Value Theorem, explain why this function has (at least)…

A: The function is  f(x)=x2-x-2

Q: Show that the function f(x) = x' + 3x² is continuous at every real number a.

A: fx=x3+3x2

Q: - Show that the function f(x) = secx.cscx odd or even

A:

Q: 18. Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1 1+(f(x))². Show…

A:

Q: Differentiate the function y = In [(x* – 1)(x² + 1)²] to the simplest form. - The number of online…

A:

Q: Let f(æ) = – 3x* In æ %3D f'(x) = f'(e²) =

A:

Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

A:

Q: Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1+ (F(x))*. What is…

A: Given that f(g(x)). = x  and f'(x)= 1+(f(x))2 and we find g'(x). Here i attached solution of this…

Q: Let f(x) = x -[r] and f :[1,5) →[0,1). What is the discontinuously type of f(x) at the point x = 3?

A:

Q: Let f (x) = x and g (x)=|x| be two real-valued functions, O (x) be a function satisfying the…

A: Introduction :

Q: Consider a function f(x) = |x – 3|. a. Show that f (x) is not differentiable at 3. -

A: Given         f(x) =|x-3|

Q: 3 Show that the function f(x) = Vx – 5 is one to one function. %3D

A: The objectives to show that the function f(x) is one to one function.

Q: (b) Use the definition in (a) to compute f'(2) for the function f(x)

A:

Q: Suppose that f(x) is a differentiable function such that f(3)= 8 and f'(3)=-2. If g(x)=xf(x), then…

A: Product Rule of differentiation : d(u.v)dx = u.dvdx + dudx.v

Q: If function g(x) =- is discontinuous at x=a, find the points of (x-a) x2 -1 (x+4)(2x-3)´…

A:

Q: What is f (3) When x²-9 X-3 f(x) = x when XX3? Assume that f(x) is a function that is continuous for…

A:

Q: and g:y → X. If gof -Ix => Show that f is one-to-one function %3D and 8 is surjective function ?

A:

Q: Find a function f(x), such that f"(x) = 3sin(4x). %3D

A:

Q: (4) Sketch the graph of a function f(x) satisfying (a) f(x) 2 and for x 0 for x between -1 and 2,…

A:

Q: Find and sketch the domain of the function f (x, y) = In(9 – x² – 9y²).

A: The given function,  f(x,y)=ln9-x2-9y2

Q: Suppose that f(x) is a differentiable function such that f(8)=5 and f(8)=0. If g(x)=sin(f(x)), then…

A:

Q: Prove that if f(x)=c (a constant function), then f'(x)= 0

A: Given query is to prove that derivative of constant function is zero.

Q: Show that the function g(x) =x |x | has an inflection point at (0,0) but  g " (0)  does not exist.

A: Given function:                                 g(x)=x|x|   To find out the Inflection point=?…

Q: Differentiate the function. f(x)  = In 1/x

A: Given: The function fx=ln1x, To find: The differentiation of given function.

Q: Determine whether the function f (x) = {: —х in — 1 <x<0 in 0<x < 1 is even or odd,

A:

Q: Suppose that f(x) is a differentiable function such that f(3)= 8 and f'(3)=2. If g(x)=xf(x), then…

A:

Q: What is f'(x) at x = -1 of the function f(x)=x^-2 + (x^2)^(1/2) *

A:

Q: C. Show that f(x) = (x26)² has no inverse on the interval (-∞,0).

A: Since you posted two questions here, i can answer only 1. Please reupload second question again.…

Q: Evaluate f''(c) at the point. f(x) = (x2 - 5)(x3- 5), c = 1

A:

Q: 1-What are Univalent Functions .

A: We define a function on complex numbers.

Q: , for x 1 Let f(x) be a function defined by f(x)=- Discuss the contuniuty of f and f'.

A:

Q: Find the domain of the function using interval notation. f (x) = -2a (x – 3) (x – 5) | | To enter…

A: soution:-f(x)=-2x(x-3)(x-5)To find the domin of f(x)The domain of a function is the set of all…

Q: Let f(x, y) = -e2"-y + In(3x – y). Find the domain of this function.

A:

Q: Express the function in the form f◦g. f(x)=sec(x2)tan(x2).

A:

Q: 3 Show that the function f(x) = Vx – 5 is one to one function.

A: The given function is: fx=x-53

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.