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By the answering guidelines of Bartleby, We can answer only first three subparts, please post other questions separately
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- 2. Let g(x)= {-1/5x + 2, x<0 -2, x=0 x+2, x>0. Does the lim g(x) x→0 exist? If yes, give its value. If not, why?1. Is it possible that f(2) = 5 but limx→2f(x) = 7? If so, what kind of function can satisfy this?Let ƒ(x) = (x2 - 1)/( | x| - 1). Make tables of the values of ƒ at values of x that approach c = -1 from above and below. Then estimate limx→ -1 ƒ(x).
- 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. 04. Given f(x)= { 1, if x < 0 x-1, if x ≥ 0 , estimate lim f(x) x→0- a.1 b. 0 c. does not exist d. -1 5. Given f(x)= { 1/x, if x < 4 x2, if x ≥ 4 , estimate lim f(x) x→4+ a. 1/4 b. 2 c. does not exist d. 161. If limit of f(x) -8/x-1=10 as x approaches 1, find limit of f(x) approaches 1 2. If limit of f(x)/x^2 = 5 , find the following limts, a) limit of f(x) as x approaches 0 and b) limit of f(x)/x as x approaches 0. 3. Show by means of an example that limit of ( f(x) +g(x) ) as x approaches zero may exist even though neither limit of f(x) approaches a nor limit of g(x) exists as x approaches a
- Determine value for c so that lim f(x) x--> 3 exists f(x)= 1/3x+c For x<3 -x+8 For x>3Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). a. Make a table of the values of h at x = 2.9, 2.99, 2.999, and so on. Then estimate limx-->3 h(x). What estimate do you arrive at if you evaluate h at x = 3.1, 3.01, 3.001,......instead? b. Support your conclusions in part (a) by graphing h near c = 3 and using Zoom and Trace to estimate y-values on the graph as x--> 3.
- 6. Given f(x)= { 3, if x < -2 x, if -2 ≤ x<8 x+3, if x≥8 estimate lim f(x) x→−2 a.-2 b. 1 c. does not exist d. 3 7. Using a table of values, estimate lim 1/ x-3 x→3 a. 1 b. -1 c. - ∞ d. ∞ 8. Using table of values, estimate lim x+4/ (x-5)2 x→5 a. 10 b. 8 c. - ∞ d. ∞Suppose g(x)<h(x)forx∈(0,1)∪(1,2) both limx→1g(x)andlimx→1h(x) exist. Must limx→1g(x)<limx→1h(x)? true or falseIs there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a exist otherwise enter 0.