Question

Evaluate the limit below. lim h?0 ( (2 + h)^2 - 4 ) / h SOLUTION If we define F(h) = ( (2 + h)^2 - 4 ) / h then we can't compute the lim h?0 F(h) by letting h = 0, because F(0) is undefined. But if we simplify F(h) algebraically, we find the following. F(h) = ( ( [ ] + 4h + 4 ) - 4 ) / h = [ ] / h = [ ] (Recall that we consider only h ? 0 when letting h approach 0.) Thus, we get the following. lim h?0 ( (2 + h)^2 - 4 ) / h = lim h?0 ( [ ] ) = [ ]

          Evaluate the limit below.
lim h?0 ( (2 + h)^2 - 4 ) / h
SOLUTION
If we define
F(h) = ( (2 + h)^2 - 4 ) / h
then we can't compute the lim h?0 F(h) by letting h = 0, because F(0) is undefined. But if we simplify F(h) algebraically, we find the following.
F(h) = ( ( [  ] + 4h + 4 ) - 4 ) / h
= [  ] / h
= [  ]
(Recall that we consider only h ? 0 when letting h approach 0.) Thus, we get the following.
lim h?0 ( (2 + h)^2 - 4 ) / h = lim h?0 ( [  ] ) = [  ]

Evaluate the limit below.
lim h?0 ( (2 + h)^2 - 4 ) / h
SOLUTION
If we define
F(h) = ( (2 + h)^2 - 4 ) / h
then we can't compute the lim h?0 F(h) by letting h = 0, because F(0) is undefined. But if we simplify F(h) algebraically, we find the following.
F(h) = ( ( [ ] + 4h + 4 ) - 4 ) / h
= [ ] / h
= [ ]
(Recall that we consider only h ? 0 when letting h approach 0.) Thus, we get the following.
lim h?0 ( (2 + h)^2 - 4 ) / h = lim h?0 ( [ ] ) = [ ]

Added by Angela R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

01/31/2023

Step 1

B: We can use the quadratic formula to find F(h). C: Show more…

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Evaluate the limit below. lim h→0 SOLUTION If we define F(h), then we can't compute the limit of F(h) by letting h = 0, because F(0) is undefined. But if we simplify F(h) algebraically, we find the following: F(h) = 4h (Recall that we consider only h approaching 0.) Thus, we get the following limit: lim h→0 4h