Question

Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.\\ $\lim_{h \to 0} \frac{(x+h)^2 - x^2}{h}$

          Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.\\
$\lim_{h \to 0} \frac{(x+h)^2 - x^2}{h}$

Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.

limh → 0((x+h)^2 - x^2)/(h)

Added by Christopher P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Suman K

06/30/2022

Step 1

Step 1: First, let's simplify the expression inside the limit: ((x+h)^(2)-x^(2))/h Expand the numerator: (x^(2) + 2xh + h^(2) - x^(2))/h Simplify by canceling out x^(2) terms: (2xh + h^(2))/h Factor out h from the numerator: h(2x + h)/h Cancel out h from the Show more…

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