-1< x< 2 3 Consider the function f(x) = x = 2 |4- x 2 < x < 3 1 x2 3 (a) Sketch f(x). (b) Discuss the existence of the following limits: lim f(x) and lim f(x). x→2 x→3 (c) State with reason whether f(x)is continuous at x = 2 and x = 3.
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- 1. Consider the function f(x)= {x+2, x>0 -x-6,x<0. Use the table of values to find the limit of the following: a. lim f(x) x→0+= x 0.0001 0.001 0.01 0.1 1 f(x) b. lim f(x) x→0-= x -1.0 -0.1 -0.01 -0.001 -0.0001 f(x) c. Does the limit f(x) x→0 exist? If yes, give its value. If not, why?Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=1. Evaluate lim (2x-5) given its graph below. x →2 a.0 b. -1 c. 2 d. 1 2. Given the graph of f(x) below, evaluate its limit as x approaches 3. a.2 b. 3 c. 1 d. 0
- 1- give an example of a function with two zeros (f(c)=0), one of which cannot be found by the bisection method (you may sketch a graph.) 2- find the constant c so that the lim_{x->3} (x^2+x+c)/(x^2-5x+6) exists. 3- determine at which points, the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q is continuous.For the function f(x) (X^2-3 if -3 ≤x2 C) is f continuous at x=2? D) does lim f(x) exist at x->4^-? E) does lim exist f(x) exist at x->4^+?f(x) = { x2 x<= -2, 4 -2<x<0, 4+x3 x>=0 Which statements are true? (i) f(x) is differntiable at x = - 2 (ii) f(x) has a limit at x = - 2 (iii) f(x) is contionous at x = - 2
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- If the limit of f(x) exists as x approaches some value, a, then the limit of f(x) x -a/x -a: a. is the same b. two of the other answers are correct c. may not exist d. does not exist because there is no hole at x = ag(x)<h(x)forx∈(0,1)∪(1,2) both limx→1g(x)andlimx→1h(x) exist. True or false?Given f(x)= ((n+1)(n+2)(n+3)....(n+2023))^(1/2023) then find lim n approaches to infinity f(x)(means find limit of f(x) when n approaches to infinity) A) DNE B) 2024 C)1012 D)2023