Suppose that the function f: [0, 1] in R is continuous and thatf(x) > 2      if 0<=X < 1.Is it necessarily the case that f ( 1) > 2?

Q: Suppose f: (0, 1)→ (0, 1) is a surjective monotonic function. True or false: The function f is…

A: f: 0,1→0,1 is a surjective monotonic function.

Q: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that f…

A: Let f:R--&gt;R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a&gt;1. Show that…

Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

A:

Q: Is there a real function f(x) that is differentiable only at a point x?

A:

Q: Suppose that f : A → B is a function, C C B and D C B. Prove that Š (C – D) = } (C) - } (D).

A: Solution :-

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: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: Let f be a function defined on [15, 23]. Suppose for every x ≤ (15, 23) d da If f(16) = 44, find the…

A: We  know By definition of derivative  in interval a,b⇒f'x=limx→afx-fax-a

Q: If f is a function that is continuous on the open interval (1, 4), then f is continuous at x = 3.…

A: Given: If f is a function that is continuous on the open interval (1,4), then f is continuous at…

Q: Give an example of an everywhere-continuous function h(r) that is differentiable at every real…

A:

Q: u(1) = 2 and u' (1) -4. Find the tangent line to the curve и(х) cos(y) — 5eV — 3. at the point…

A:

Q: f(2) = 4 and f(3) = 3. With this information, can you determine whether there exists a real number c…

A:

Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

A:

Q: d dx y' z' y" z"

A:

Q: Let f(x) = x. Show directly that f ∊ R[0, 2]

A:

Q: Suppose that u(x) is a differentiable function such that

A:

Q: Consider the function f with domain (-2, : 3|22 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

A:

Q: Let f be a function defined on [11, 25]. Suppose for every x = (11, 25) d. dx -f(x) = 0. If f(12) =…

A: Given query is to find the value o f(24).

Q: The function f(x) = 1/ (x 4 + 6) is continuous for all values of x in R. %3D O False O True

A: We have to determine whether the given function is continous for all values of x in R or not.

Q: 호호 -^ z-vz44 Z

A:

Q: Since f(x) is continuous between a and b, the function needs to cross the x-axis. O TRUE O FALSE O…

A: Given fx is continuous between a and b

Q: Let f be a real-valued function on R. Suppose that f(−1) = 3 and f'(x) ≤ 2 for all values of x. How…

A: f(-1)=3f'(x)≤2Integrating w.r.t x;∫ f'(x) dx ≤ ∫2 dxf(x)≤2x+Cf(-1)=33=2(-1)+CC=3+2C=5

Q: For what values of x are the following functions NOT continuous. 4x² – 17x + 15 (x) = Vx² – 25 b.…

A:

Q: Let f :[-2,6] R be the function given by * if - 2sx<0 if 0sx< 2 4 -x if 2 sxs6. f(x) = 2.x For each…

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.