Estimate the limit numerically. $$\lim _ { x \rightarrow + \infty } \frac { 6 x ^ { 4 } + 17 x ^ { 3 } } { 1,447 x ^ { 6 } + 7 }$$
A) $+ \infty$
B) $- \infty$
C) 0
D) $\frac { 1 } { 1,447 }$
E) 1

Question

Estimate the limit numerically.   $$\lim _ { x \rightarrow + \infty } \frac { 6 x ^ { 4 } + 17 x ^ { 3 } } { 1,447 x ^ { 6 } + 7 }$$  
A) $+ \infty$
B) $- \infty$
C) 0
D) $\frac { 1 } { 1,447 }$
E) 1

Quizplus · Accepted Answer

When $x$ approaches $+\infty$, the highest degree term in the denominator (which is $x^6$) dominates the behavior of the function, making the value of the fraction approach 0. The terms in the numerator grow at a slower rate compared to the $x^6$ term in the denominator.

Estimate the Limit Numerically lim⁡x→+∞6x4+17x31,447x6+7\lim _ { x \rightarrow + \infty } \frac { 6 x ^ { 4 } + 17 x ^ { 3 } } { 1,447 x ^ { 6 } + 7 }x→+∞lim​1,447x6+76x4+17x3​

Estimate the Limit Numerically $\lim _ { x \rightarrow + \infty } \frac { 6 x ^ { 4 } + 17 x ^ { 3 } } { 1,447 x ^ { 6 } + 7 }$