true or false questions. please explain why.  . 1-if lim_{x->a} f(x)=∞ and y=g(x) is defined and bounded below on an interval containing a , then lim_{x->a} f(x)+g(x)=∞ 2- if 0≤a≤1/e , then the equation x.e^-x=a has a nonnegative solution. 3-suppose that a function y=f(x) is continuous on I=[a,b] and if the set  f(I)=[f(a),f(b)], then y=f(x) is strictly increasing.

Q: The sales of a book publication are expected to grow according to the function S=…

A: Given,           The sales of a book publication are expected to grow according to the function S=…

Q: p(x)=3x^2-x+8, million dollars is a company’s profit, x years after 2000,   0≤x≤10 Find the…

A: Hey, since there are multiple sub-parts posted, we will answer the first 3 sub-parts. If you want…

Q: Use the definition of a limit to show that (i) limx→0 (x^2 + 6x + 9) = 9 (ii) limx→−7 and…

A: Authoring guidelines:…

Q: Let h(x)= (x^2-9)/(x^2-3x) a/ what interval is h(x) continuous? b/ evaluate the following.…

A:

Q: and 2(x)=そ + f(x):1/m2x) メー< K- ? (Drag and d rop the correct option in the given box) X-2 x2 lexf…

A:

Q: f'(x) = (x-1)(x-2)(x-3)(x-4)   What can be said about lim(x->infinity) if anything

A: Answer and explanation is given below

Q: True or False: When lim,a f (x) exists, it always equals f (a). O True. The apparent destination of…

A: The statement is given by When limx→afx exists, it is always equal to fa

Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: 2.3 Q14

A: The objective of this question is to find the limit of the function f(x) as x approaches 2, given…

Q: The limit lim h→0 f(x) a = 1 = x^3 (1 + h)³ - 1 h represents f' (a) for some function f and some…

A: We know that: f'(x)=limh→∞f(x+h)-f(x)h and f'(a)=limh→∞f(a+h)-f(a)h.

Q: Show that lim n-&gt;∞ (1 + x/n)^ n = e^x for any x

A: Express (1+ x/n)^n using e in the base

Q: 4x + 6 x -5

A: Given query is to find indicated limits.

Q: 1) Let f(x) be the function shown. (Answer "DNE" if the limit does not exist). (a) Find_lim_ f(x) =…

A: solution of function is given below..

Q: then A(-2u - 20) = -2 ---B 5 and Au 3 Au = 2 4

A:

Q: give an example of a function with two zeros  (f(c)=0), one of which cannot be found by the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Evaluate the following limits. A.) limx->infinity8/(e^x-8)= B.) limx->-infinity8/(e^x-8)=

A: we have to find limit

Q: 3. A function f(x) is defined as follows. (x + 2 x<-1 f(x) = } Ax? -1<x<1 x21 where k is constant.…

A:

Q: 12-Determine the equation of any asymptote and coordinate of holes for F(x)= -12x^3 +44x^2 -32x -16…

A: The function is

Q: For the function A whose graph is shown, state the following. (If the limit is infinite, enter 'o'…

A: If x approaches a from the right hand side, then it can be denoted using the limit: limx→a+. If x…

Q: Determine the value of 6>0 for which lim (3x -1)=47 X4 A 6 = max{-4-16 -, -4+, 16 + | 3 6 =…

A: Given: limx→43x2-1=47 and δ&gt;0

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.