1.) lim(x – 2) x-7 limit from the left f(x) limit from the right f(x) 6. 6.5 8. 7.5 6.99 7.1 6.9999 7.001 lim (x – 2) = X→7- lim (x – 2) = lim(x – 2) = X-7 f (7) =
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complete the table of values then evaluate the limits and function of value
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- - determine the limit lim_{h->0}[(x+h)2-x^2]/h by treating x as a constant. - determine the lim_{x->0} cos(2x)/x -determine the limit_{x->0} sin(2x^2)/xtan(4x) thanks...3. Calculate the limits(a) lim (1-cosx)/(5sinx) x->0 (b) lim (x^10)/(10^x) x->inf1. Broadly speaking, what are the Limit Laws, and why do they help us calculate limits?2. In Example 3, there is a step where the function x2 − 1x − 1is changed to x+ 1. But unlike the secondfunction, the first function is undefined at x = 1. How can we justify changing functions this way?3. Explain the flaw in the following calculation:limx→0x2sin(1/x) = (limx→0x2) · (limx→0sin(1/x)) = 0 · (limx→0sin(1/x)) = 0.
- lim f(x) x--> 3, where f(x) = {2(x+1), if x < 3 or 4, if x = 3, or x^2 - 1, if x > 3} piecewise.they have the limit as 8? why?1. 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 ageneral question on why is the lim of x approaches positive infinity of ekx /xn =infinity and lim of x approaching negative infinity xn e-kx =0