Evaluate the limit: $$\lim _ { x \rightarrow \frac { \pi } { 2 } } \left\langle t ^ { 2 } , \cos ( t ) \right\rangle$$ A) $$ B) $\langle 0,1 \rangle$ C) $$ D) $\left.

Question

Evaluate the limit: $$\lim _ { x \rightarrow \frac { \pi } { 2 } } \left\langle t ^ { 2 } , \cos ( t ) \right\rangle$$ A) $< 0 , \frac { \pi ^ { 2 } } { 2 } >$ B) $\langle 0,1 \rangle$ C) $< \frac { \pi ^ { 2 } } { 4 } , - 1 >$ D) $\left. < \frac { \pi ^ { 2 } } { 4 } , 0 \right\rangle$

Quizplus · Accepted Answer

The limit of the first component $t^2$ as $t$ approaches $\frac{\pi}{2}$ is $\left(\frac{\pi}{2}\right)^2 = \frac{\pi^2}{4}$. The limit of the second component $\cos(t)$ as $t$ approaches $\frac{\pi}{2}$ is $\cos\left(\frac{\pi}{2}\right) = 0$. Therefore, the limit of the vector is $\left<\frac{\pi^2}{4}, 0\right>$.

Evaluate the Limit lim⁡x→π2⟨t2,cos⁡(t)⟩\lim _ { x \rightarrow \frac { \pi } { 2 } } \left\langle t ^ { 2 } , \cos ( t ) \right\ranglex→2π​lim​⟨t2,cos(t)⟩

Evaluate the Limit $\lim _ { x \rightarrow \frac { \pi } { 2 } } \left\langle t ^ { 2 } , \cos ( t ) \right\rangle$