Consider $\lim _ { b \rightarrow \infty }$ $\frac { 2 b - 1 } { b }$ . Which of the following is true?
A) The limit exists and is equal to zero.
B) none of these
C) The limit exists and is equal to one.
D) The limit diverges.
E) The limit exists and is equal to two.
Evaluate the improper integral whenever it is convergent. If it is divergent, state this.

Question

Quizplus · Accepted Answer

The limit can be simplified by dividing both the numerator and the denominator by $b$, resulting in $\lim _ { b \rightarrow \infty }$ $\frac { 2 - \frac{1}{b} } { 1 }$. As $b$ approaches infinity, $\frac{1}{b}$ approaches 0, leaving the limit as 2.

Consider lim⁡b→∞\lim _ { b \rightarrow \infty }limb→∞​ 2b−1b\frac { 2 b - 1 } { b }b2b−1​

Consider $\lim _ { b \rightarrow \infty }$ $\frac { 2 b - 1 } { b }$