Suppose that f (0) = 2 and f'(x) < 3 for all x > 0. Show that f(4)< 14 by considering f on the interval I = [0,4]. Show that f(x) < 2 + 3x for any x > 0.

Q: Find f-1 if f (z) = iz + 1.

A:

Q: Let f and g be functions of x, where a is an unknown constant. What is a valid expression for (-)'…

A:

Q: Find max and min of function on the interval    f(x)=-x4-x3+5x2-4 on [-2,1]

A: The given function is; f(x)=-x4-x3+5x2-4 on [-2,1]

Q: Find f g and g of, where f (x) = x^2 + 1 and g(x) =3x + 2, are functions from R to R.

A:

Q: 4(a). Define the zeroth divided difference by f[x,]= f (x; ). Write the expressions for the first…

A: As many questions are given and its various subparts, I will solve only the first. Zeroth divided…

Q: Find the constants a and b such that the function is continuous on the entire real line x 3 a = b =

A:

Q: determine at which points, the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q is continuous.

A: Given To evaluate the points where the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q    is…

Q: If f(x) = ax , show that f( - x) = 1 / f(x) .

A: We have to show that: f-x=1fx Where given function is fx=ax. Taking LHS (putting x=-x in fx ), we…

Q: Consider the piecewise function 1 3.x if x < -2 f (x) = ax2 + 2x + b if – 2 < x Where a and b are…

A:

Q: f(x)= 23-4b            If x=3

A: Continuity: A real function f(x) is said to be continuous at a∈R (R− is the set of real numbers), if…

Q: Find f. f"(x)  =x6 - 4x4 +x +1

A: ∫xndx = xn+1n+1+C

Q: Let X=[-1,1] and Y=[0,1], and define the function f:X-->Y by f(x)=x^2. Which of the following is NOT…

A:

Q: If f(x)= anx", specify the domain of f.

A:

Q: Consider the function f(x)=x/x^2+12x+32. Determine the intervals on which f is increasing and…

A: We have to determine the intervals at which the function  is increasing or decreasing.

Q: Find f"(0) for the function f(x) = (x+1)e².

A: Given query is to find the Indicated derivative

Q: 4. xy+2x D /y

A: Solution:Given xy+2x =yTo differentiate explicitly with respect to x.Formula:(uv)'=uv'+u'v

Q: Find all the derivatives of f, given f(x) = x8 – 5x7 + 4x6 – nx* + 3x³ + 11.

A:

Q: Find the domain of f

A: Given  fx=x+1x3-4x To find the domain of f(x)

Q: Help find a function f so that f ‘(x) = 3x2+ 2x+5 and f (1) = 10

A:

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.