Answer: Given limit, $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} {\left( {\cos x + a\sin bx} \right)^{1/x}} \end{array}$ ...
Evaluate the following limit:
Answer: Given limit, $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} {\left( {\cos x + \sin x} \right)^{1/x}}\\ \end{array}$ f (x) = cos x + sin x – 1 g (x) =...
Evaluate the following limit:
Answer: Given limit, $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} {\left( {\cos x} \right)^{1/\sin x}}\\ \end{array}$
Evaluate the following limit:
Answer: Given limit, $\begin{array}{l} \mathop {\lim }\limits_{x \to {0^ + }} {\left\{ {1 + {{\tan }^{\sqrt x }}} \right\}^{1/2x}}\\ \end{array}$
Evaluate the following limit:
Answer: Given limit, $\begin{array}{l} \mathop {\lim }\limits_{x \to \pi } {\left( {1 - \frac{x}{\pi }} \right)^2}\\ \end{array}$
Evaluate the following limit
Solution: As per the given question,
Evaluate the following limit
Solution: As per the given question,
Evaluate the following limit
Solution: As per the given question,
Evaluate the following limit
Solution: As per the given question,
Evaluate the following limit
Solution: As per the given question,
Let the limit given below
Solution: As per the given question,
Let f(x) be a function defined by given below limit . Then show that lim x-> 0 f(x) doest not exist.
Solution: As per the given question,
Show that the given limit does not exist
Solution: As per the given question,
Solve:
Solution: As per the given question, So, let \[x\text{ }=\text{ }2\text{ }-\text{ }h,\text{ }where\text{ }h\text{ }=\text{ }0\] Substituting the value of \[x,\]we get
Show that the given limit does not exist
Solution: As per the given question,
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
∴ The value of the given limit is \[1/2\]
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
We need to find the limit of the given equation when \[x\text{ }=>\text{ }0\] Now let us substitute the value of x as \[0\], we get an indeterminate form of \[0/0\]. Let us rationalizing the...
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
Evaluate the following limits:
∴ The value of the given limit is \[1/2\]