Determine the limit of each function analytically. Show neat and complete soluti

Question

Determine the limit of each function analytically. Show neat and complete solution. (hint: some of the items need to be factored or rationalized for the limits to exist)

lim_{h \to 0} \frac{{(1 + h)}^{2} - 1^{2}}{h}

Answer 1

Given:
Find the limit of:

lim_{h \to 0} \frac{{(1 + h)}^{2} - 1^{2}}{h}

Solution:

lim_{h \to 0} \frac{{(1 + h)}^{2} - 1^{2}}{h} = lim_{h \to 0} \frac{(1 + h + 1) (1 + h - 1)}{h}

[∴ (a^{2} - b^{2}) - (a + b) (a - b)]

= lim_{h \to 0} \frac{(h + 2) (h)}{h}

= lim_{h \to 0} (h + 2)

= 0 + 2

lim_{h \to 0} \frac{{(1 + h)}^{2} - 1^{2}}{h} = 2

Answer 2

Jeffrey Jordon

Answered 2022-07-05 Author has 2313 answers

Answer is given below (on video)

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Determine the limit of each function analytically. Show neat and complete soluti

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