O 9 a, b E IR and aab onyway. f: (0.1) (a.b) Xnf(x) = at (b-a) X, for Hx e(o, 1), Show that the fonction f, which is defined as, is (f(x) 2a+ (b-a)x) One to on e and Coversug b) Do intervals (0,1) and inter vals (a,b) have the Same Streng th ? why is that?

Q: 2. Find the intervals of increase or decrease. a) ƒ(x)=x ln x b) f(x) = xe* c) f(x) = xe¯* d) ƒ(x) =…

A:

Q: the domain of f' in interval notation Ans 7d D = f-1 e. the range off' in interval notation ans 7e…

A: f(x) = x-235inverse y = x-235interchange x and y x = y-235solve for y y = 25x2+23f-1(x) = 25x2+23

Q: 1 = x² +1 1. Use the ed definition to prove that the function f(x) = (a) continuous at x = 0. (b)…

A:

Q: Consider the function f(x) that is described by the statment: “ the function decreases to the point…

A: Explanation of the answer is as follows

Q: The function f(x) = 2 + 1/x is continuous on the following interval EXCEPT. O a. [-2,-1] O b. [1,2]…

A: At any point a for a function f(x) the limit limx→afx=L exists if the limx→a−fx=limx→a+fx=fa.

Q: Let P(s) be the function - 1. Find the following: | s+1 P(7) = %3D P(- 9) = %3D P() - %3D 8. In each…

A: Since, you have posted question with multiparts. As per guidelines we"ll solve only first three…

Q: Find all intervals where the function f(x) = x+ x- x is increasing.

A:

Q: Which among the interval whose f(x) is increasing? а. (0,5) b. (-4,0) с. (5,7) d. (-7,-4) e. None of…

A: The function y=fx is an increasing function if x increases then y also increases. that means if we…

Q: Zx? +5x-75 Let fl)- X-5 a that f hgs a femovable disqontinutyy at 5 d delermine the value for HS)…

A:

Q: Stample? bet ftz)= if Show that a)f(2)is Continuous everyulhere on- 7 the Comptex derivative fo)…

A: Like a real-valued function, a complex-valued function can also be continuous and differentiable. A…

Q: 4. Use the fplot command to plot the function f(t) lcos(3x)+ sin (4x) in the domain -25 x S2. %3D

A:

Q: x2+2x+5. Show, x+2 Q1 Let f: R\ {-2} → R be given by f(x) directly from the definition, that f is…

A:

Q: Decide if f(x) is uniformly continuous on the interval. Explain

A:

Q: Let f(x) = (4x – 6)(x² – 5). Find all the values of x for which f'(x) = 0. Present your answer as a…

A: Given fx=4x-6x2-5

Q: What is the range of the function y=f(x) =2sin 57 A [-3,7] B B [-7,-3] В © [-7,3] D D [3,7]

A: We have to find range of give function.

Q: Q5. Explain why f(x) is not continuous at a. x2 - 25 f(x) = x + 5 if x #-5 a = - 5 if x =-5

A:

Q: Let f(x) = vV72 – x and g(x) = x² – x. Give the domain of f o gusing interval notation.

A:

Q: -2 -1 0 -1- 1 2 3 4 5 6 7 8 9 10 X Find the domain of the function fo g. (Give your answer as an…

A: domain of   f∘g=domain of  g(x)domain of  g(x)=[0,6]domain of   f∘g=domain of  g(x)=[0,6]

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.