1316 (i) Make a guess at the limit (if it exists) by evaluating the function at the

Chapter 1, Problem 14

(choose chapter or problem)

(i) Make a guess at the limit (if it exists) by evaluating the function at the specified \(x\)-values. (ii) Confirm your conclusions about the limit by graphing the function over an appropriate interval. (iii) If you have a CAS, then use it to find the limit. [Note: For the trigonometric functions, be sure to put your calculating and graphing utilities in radian mode.]

(a) \(\lim _{x \rightarrow 0} \frac{\sqrt{x+1}-1}{x} ; x=\pm 0.25, \pm 0.1, \pm 0.001\)

                                          \(\pm 0.0001\)          

                                   

(b)  \(\lim _{x \rightarrow 0^{+}} \frac{\sqrt{x+1}+1}{x} ; x=0.25,0.1,0.001,0.0001\)        

(c) \(\lim _{x \rightarrow 0^{-}} \frac{\sqrt{x+1}+1}{x} ; x=-0.25,-0.1,-0.001\)

                                           \(-0.0001\)                                                  

Equation Transcription:

 

   

 ,

Text Transcription:

x

lim_x right arrow 0 square root x+1 -1/x; x= +_- 0.25, +_- 0.1, +_- 0.001,

+_-0.0001

lim_x right arrow 0_+  square root x+1 -1/x; x= +_- 0.25,0.1,0.001,0.0001

 lim_x right arrow 0_- square root x+1 -1/x; x= -0.25,-0.1,-0.001,

-0.0001