Guess the value of the limit ( it it exists) by evaluationg the funciton at the given numbers ( correct to six decimal places)a) lim x 2 − 2 x / x 2 − x − 2 , x = 2.5 , 2.1 , 2.05 , 2.01 , 2.005 , 2.001 , 1.9 , 1.95 , 199 , 1.995 , 1.999 x → 2b) lim x 2 − 2 x / x 2 − x − 2 , x = 0 , − 0.5 , − 0.9 , − 0.95 , − 0.99 , − 0.999 , − 2 , − 1.5 , − 1.1 , − 1.01 , − 1.001 x → − 1

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Guess the value of the limit ( it it exists) by evaluationg the funciton at the given numbers ( correct to six decimal places)a)   lim      x          2        −  2  x      /        x          2        −  x  −  2  ,  x  =  2.5  ,  2.1  ,  2.05  ,  2.01  ,  2.005  ,  2.001  ,  1.9  ,  1.95  ,  199  ,  1.995  ,  1.999  x  →  2b)   lim      x          2        −  2  x      /        x          2        −  x  −  2  ,  x  =  0  ,  −  0.5  ,  −  0.9  ,  −  0.95  ,  −  0.99  ,  −  0.999  ,  −  2  ,  −  1.5  ,  −  1.1  ,  −  1.01  ,  −  1.001  x  →  −  1

agergadas3b · Accepted Answer

a)   lim      x          2        −  2  x      /        x          2        −  x  −  2  ,  x  =  2.5  ,  2.1  ,  2.05  ,  2.01  ,  2.005  ,  2.001  ,  1.9  ,  1.95  ,  199  ,  1.995  ,  1.999  x  →  2  f  (  x  )  =  (      x          2        −  2  x  )      /    (      x          2        −  x  −  2  )f(2.5)=0.714286f(2.1)=0.677419f(2.05)=0.672131f(2.01)=0.667774f(2.005)=0.667221f(2.001)=0.666778f(1.9)=0.655172f(1.95)=0.661017f(1.99)=0.665552f(1.995)=0.66611f(1.999)=0.666556          lim      x          2        −  2  x      /        x          2        −  x  −  2  =  2      /    3  x  →  2b)   lim      x          2        −  2  x      /        x          2        −  x  −  2  ,  x  =  0  ,  −  0.5  ,  −  0.9  ,  −  0.95  ,  −  0.99  ,  −  0.999  ,  −  2  ,  −  1.5  ,  −  1.1  ,  −  1.01  ,  −  1.001  x  →  −  1  f  (  x  )  =  (      x          2        −  2  x  )      /    (      x          2        −  x  −  2  )f(0)=0f(-0.5)=-1f(-0.9)=-9f(-0.95)=-19f(-0.99)=-99f(-0.999)=-999f(-2)=2f(-1.5)=3f(-1.1)=11f(-1.01)=101f(-1.001)=1001

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