Given that $\lim _ { x \rightarrow c } f ( x ) = 7 , \text { and } \lim _ { x \rightarrow c } g ( x ) = 3$ ,find $\lim_{x \rightarrow c} h ( x ) = [ f ( x ) + g ( x ) ] ^ { 2 }$ .
A)42
B)100
C)63
D)limit does not exist
E)147

Question

Quizplus · Accepted Answer

The limit of a sum is the sum of the limits, so $\lim_{x \rightarrow c} [f(x) + g(x)] = 7 + 3 = 10$. Therefore, $\lim_{x \rightarrow c} [f(x) + g(x)]^2 = 10^2 = 100$.

Given That lim⁡x→cf(x)=7, and lim⁡x→cg(x)=3\lim _ { x \rightarrow c } f ( x ) = 7 , \text { and } \lim _ { x \rightarrow c } g ( x ) = 3limx→c​f(x)=7, and limx→c​g(x)=3

Given That $\lim _ { x \rightarrow c } f ( x ) = 7 , \text { and } \lim _ { x \rightarrow c } g ( x ) = 3$