Question

66. Which of the following is not an indeterminate form (a) 0⁰ (b) 0^∞ (c) ∞^⁰ (d) 1^∞​

Answer 1

Answer:

b)0^infinity

Step-by-step explanation:

There are seven indeterminate forms which are typically considered in the literature:

{\displaystyle {\frac {0}{0}},~{\frac {\infty }{\infty }},~0\times \infty ,~\infty -\infty ,~0^{0},~1^{\infty },{\text{ and }}\infty ^{0}.}{\displaystyle {\frac {0}{0}},~{\frac {\infty }{\infty }},~0\times \infty ,~\infty -\infty ,~0^{0},~1^{\infty },{\text{ and }}\infty ^{0}.}

Answer 2

(b) $0^{\infty}$

Of the given options, (b) $0^{\infty}$ is not an indeterminate form.

Explanation:

• There are some limits of algebraic expressions in mathematical analysis, whose value cannot be determined by substitution. Not even a sufficient information can be found. That expression is called an indeterminate form.

• However there are seven indeterminate forms. They are: $\dfrac{0}{0}$, $\dfrac{\infty}{\infty}$, $0\times\infty$, $\infty-\infty$, $0^{0}$, $1^{\infty}$ and $\infty^{0}$.

• For $\dfrac{x}{x^{3}}$, when $x\to 0$, we find the indeterminate form $\dfrac{0}{0}$.

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