la). Show that f (x)3(x-2)-Inx=0 has at least one root between 1 and 2. !3!

Q: Let S be the part of the graph of the function x² + y² that lies above the disk x² + y² ≤ 4. What is…

A: The surface is the part of z=x2+y2:

Q: Let x, y be real numbers such that xy=1x and x≠y. Prove that x^2+y^2≥2\sqrt{2}|x−y|.

A: Given: xy=1x,x≠y To find: x2+y2≥22x-y

Q: For the function f(x) = 5x° -4x +2x + 3, findf "(x). Then find f"(0) and f"(4). f"(x) = Select the…

A: Double derivative

Q: 77. Show that if f is a quadratic polynomial, then the SDQ at x = a (for any h + 0) is equal to…

A:

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: 7. Suppose f(x) = x³ – 27x + 1. Prove that f has exactly one root (zero) in the interval [0, 2].

A:

Q: 2. We want to integrate a function over the region bounded by x = y2 - 1 and x = /1- y2. What should…

A:

Q: Use the function f(x) = 5x – 6 to compute and expand and simplify the following. a. f(-) = b. f(-6a)…

A:

Q: Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x^2 + 1. Compute the following: A. f(g(-3)) B. f(h(7))…

A: I have given the answer in the next step. Hope you understand that

Q: find all pairs (m, n) of positive integers such that ϕ(ϕ(n^m)) = n, where ϕ(n) is Euler's totient…

A:

Q: Find two positive numbers whose product is a such that their sum is minimum.

A: Let the two numbers are x and y So, xy=a y=a/x   Their sum= S= x+y We have to minimize S

Q: Let S be the part of the graph of the function x² + y² that lies above the disk x² + y² ≤ 4. What is…

A: The surface is the part of z=x2+y2:

Q: 3. (a) Find a unit in Z[√2] which is not equal to 1 or -1. Hint: Use 1 (b). (b) (*) Show that Z[√2]…

A: The objective of the question is two-fold. First, we need to find a unit in the ring Z[sqrt(2)] that…

Q: Z is the set of integers, R is the set of real numbers. 1) Functions f, g, h are defined as f: R ->…

A:

Q: Z is the set of integers, R is the set of real numbers. 3) Each function f is defined as f: R -> R.…

A: The objective is to find the function is one-one or not one-one. (a) fx=x+1x-1for all real numbers x…

Q: Let A =[1 -1]            [2 0] and --->x =[ i]                  [1 + i] . SHOW that Re (A--->x )…

A:

Q: Which function grows faster as O x → +∞ ? 3x¹ + 2x³ + 3x² +1 x³ ln(x² + 1)

A:

Q: |u|> c is true for all real numbers if c _ 0.

A: |u|>c is true for all real numbers if c ____ 0.

Q: 2. Let f(x)=√(x+7) for x≥-7. a) Find f-1(3). b) Let g be a function such that g-1exists for all…

A:

Q: Prove that f(x)=4x-2^2x has at least one real zero in the interval [1,2] without actually solving…

A: The given data is: Prove that fx=4x-22x has at least one real zero in the interval 1,2 without…

Q: Let 43^(55) + 55^(43)= 7q+r, where q and r are two integers such that 0<=q<7. Then r is equal to?

A: Let 43^(55) + 55^(43) = 7q +r, where q and r are two integers such that 0&lt;=q&lt;7. Then find the…

Q: locate the absolute extrima of the function 40x/x^2+25 on the closed interval [-40,40],

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.