Determine the value of the limit $\lim _ { x \rightarrow \infty } x ^ { 2 } 2 ^ { - x } .$ ?
A) $- \infty$
B)-1
C)1
D)0
E) $\infty$

Question

Quizplus · Accepted Answer

As $x$ approaches infinity, $x^2$ grows without bounds, but $2^{-x}$ (which is the same as $1/2^x$) decreases towards 0 at an exponential rate. The exponential decrease dominates the quadratic increase, causing the overall expression to approach 0.

Determine the Value of the Limit lim⁡x→∞x22−x.\lim _ { x \rightarrow \infty } x ^ { 2 } 2 ^ { - x } .limx→∞​x22−x.

Determine the Value of the Limit $\lim _ { x \rightarrow \infty } x ^ { 2 } 2 ^ { - x } .$