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Let $f(x) = \begin{cases} \sqrt{-2-x} + 5 & \text{if } x < -3\\ 15 & \text{if } x = -3\\ 2x + 14 & \text{if } x > -3 \end{cases}$ Calculate the following limits. Enter \text{``DNE''} if the limit does not exist. $\lim_{x \to -3^{-}} f(x) = \text{________}$ $\lim_{x \to -3^{+}} f(x) = \text{________}$ $\lim_{x \to -3} f(x) = \text{________}$

          Let $f(x) = \begin{cases} \sqrt{-2-x} + 5 & \text{if } x < -3\\ 15 & \text{if } x = -3\\ 2x + 14 & \text{if } x > -3 \end{cases}$ Calculate the following limits. Enter \text{``DNE''} if the limit does not exist. $\lim_{x \to -3^{-}} f(x) = \text{________}$ $\lim_{x \to -3^{+}} f(x) = \text{________}$ $\lim_{x \to -3} f(x) = \text{________}$
        
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Let f(x) = √(-2-x) + 5    if  x < -3
 15    if  x = -3
 2x + 14    if  x > -3 Calculate the following limits. Enter “DNE” if the limit does not exist. limx → -3^- f(x) = limx → -3^+ f(x) = limx → -3 f(x) =

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Let f(x)={(sqrt(-2-x)+5 if x<-3),(15 if x=-3),(2x+14 if x>-3):} Calculate the following limits. Enter "DNE" if the limit does not exist. lim_(x->-3^(-))f(x)= lim_(x->-3^(+))f(x)= lim_(0)f(x)= V-2-x+5ifx<-3 Let f(x)= 15 ifx=-3 2x+14 if x>-3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x= 3 lim f(x) +84 lim fx=
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Transcript

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00:01 In this question, we need to evaluate the following limit.
00:03 So let us see how we are going to do this.
00:05 First of all, we have been given that limit as extending to four f of x, it is already given as three.
00:14 Okay, so first part is to evaluate limit extending to four f of x whole cube.
00:24 So this is same as limit extending to four of f of x and whole cube we can apply here.
00:34 So this will be what three cubedest, so which is equals to 27.
00:40 Now let us move to the next part.
00:42 In the next part, we have to evaluate limit as extending to four of f of x square minus x squared divided with f of x plus x.
00:58 Okay, so we can and use this identity, a square minus b square is a plus b and a minus b.
01:07 Okay.
01:08 So with this what we get, we get limit extending to four, f of x plus x and another bracket, we get f of x minus x divided with f of x plus x...
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