[tex]\huge\mathcal {♨ANSWER♥}[/tex]
The term "Indeterminate" means an unknown value. The indeterminate form is a mathematical expression that means that we can't be able to determine the original value even after the substitution of the limits. There are seven indeterminate forms. They are,
1) Infinity over infinity
[tex] \frac{ \infty }{ \infty } [/tex]
conditions:
[tex]lim \: f(x) \: =\infty \: \: \: lim \: g(x) \: =\infty \\ x -> c \: \: \: \: \: \: \: \: \: \:\: \: x - > c \: \: \: \: \: \: [/tex]
2)Zero over zero
[tex] \frac{0}{0} [/tex]
conditions:
[tex]lim \: f(x) \: = 0 \: \: \: lim \: g(x) \: = 0 \\ x -> c \: \: \: \: \: \: \: \: \: \:\: \: x - > c \: \: \: \: \: \: [/tex]
3)Infinity minus infinity
[tex] \infty - \infty [/tex]
conditions:
[tex]lim \: f(x) \: = 1 \: \: \: lim \: g(x) \: = \infty \\ x -> c \: \: \: \: \: \: \: \: \: \:\: \: x - > c \: \: \: \: \: \: [/tex]
4)Zero times infinity
[tex]0 \times \infty [/tex]
conditions:
[tex]lim \: f(x) \: =0 \: \: \: lim \: g(x) \: = \infty \\ x -> c \: \: \: \: \: \: \: \: \: \:\: \: x - > c \: \: \: \: \: \: [/tex]
5)Zero to the power of zero
[tex] {0}^{0} [/tex]
conditions:
[tex]lim \: f(x) \: =0 \: \: \: lim \: g(x) \: =0 \\ x -> c \: \: \: \: \: \: \: \: \: \:\: \: x - > c \: \: \: \: \: \: [/tex]
6)Infinity to the power of zero
[tex] { \infty }^{0} [/tex]
conditions:
[tex]lim \: f(x) \: = \infty \: \: \: lim \: g(x) \: = \infty \\ x -> c \: \: \: \: \: \: \: \: \: \:\: \: x - > c \: \: \: \: \: \: [/tex]
7)One to the power of infinity
[tex] {1}^{ \infty } [/tex]
conditions:
[tex]lim \: f(x) \: = \infty \: \: \: lim \: g(x) \: =0 \\ x -> c \: \: \: \: \: \: \: \: \: \:\: \: x - > c \: \: \: \: \: \: [/tex]
☆...hope this helps...☆
_♡_mashi_♡_
