Classes

Second Year Math Functions and Limits


Change the way you learn with Maqsad's classes. Local examples, engaging animations, and instant video solutions keep you on your toes and make learning fun like never before!

Class 9Class 10First YearSecond Year
Example3:limxaxnanxawithnNExample3: \lim _{x \rightarrow a} \frac{x^{n}-a^{n}}{x-a} with n \in \mathbb{N}

4. Express each limit in terms of e :\[\text { (x) } \operatorname{Lim}_{x \rightarrow 0} \frac{e^{1 / x}-1}{e^{1 / x}+1} x<0\]
4. Express each limit in terms of  e  :\[\text { (x) } \operatorname{Lim}_{x \rightarrow 0} \frac{e^{1 / x}-1}{e^{1 / x}+1} x<0\]

4. Express each limit in terms of e :\[\text { (x) } \operatorname{Lim}_{x \rightarrow 0} \frac{e^{1 / x}-1}{e^{1 / x}+1} x<0\]

Example 1:Graph the circle x^{2}+y^{2}=4
Example 1:Graph the circle  x^{2}+y^{2}=4

Example1:Graphthecirclex2+y2=4Example 1:Graph the circle x^{2}+y^{2}=4

4. Express each limit in terms of e :(ix) \operatorname{Lim}_{x \rightarrow \infty}\left(\frac{x}{1+x}\right)^{x}
4. Express each limit in terms of  e  :(ix)  \operatorname{Lim}_{x \rightarrow \infty}\left(\frac{x}{1+x}\right)^{x}

4.Expresseachlimitintermsofe:(ix)Limx(x1+x)x4. Express each limit in terms of e :(ix) \operatorname{Lim}_{x \rightarrow \infty}\left(\frac{x}{1+x}\right)^{x}

1. Evaluate each limit by using theorems of limits:(v) \operatorname{Lim}_{x \rightarrow 2}\left(\sqrt{x^{3}+1}-\sqrt{x^{2}+5}\right)
1. Evaluate each limit by using theorems of limits:(v)  \operatorname{Lim}_{x \rightarrow 2}\left(\sqrt{x^{3}+1}-\sqrt{x^{2}+5}\right)

1.Evaluateeachlimitbyusingtheoremsoflimits:(v)Limx2(x3+1x2+5)1. Evaluate each limit by using theorems of limits:(v) \operatorname{Lim}_{x \rightarrow 2}\left(\sqrt{x^{3}+1}-\sqrt{x^{2}+5}\right)

Example 1: Determine whether \operatorname{Lim}_{x \rightarrow 2} f(x) and \operatorname{Lim}_{x \rightarrow 4} f(x) exist when\[f(x)=\left\{\begin{array}{rcc}2 x+1 & \text { if } & 0 \leq x \leq 2 \\7-x & \text { if } & 2 \leq x \leq 4 \\x & \text { if } & 4 \leq x \leq 6\end{array}\right.\]
Example 1: Determine whether  \operatorname{Lim}_{x \rightarrow 2} f(x)  and  \operatorname{Lim}_{x \rightarrow 4} f(x)  exist when\[f(x)=\left\{\begin{array}{rcc}2 x+1 & \text { if } & 0 \leq x \leq 2 \\7-x & \text { if } & 2 \leq x \leq 4 \\x & \text { if } & 4 \leq x \leq 6\end{array}\right.\]

Example 1: Determine whether \operatorname{Lim}_{x \rightarrow 2} f(x) and \operatorname{Lim}_{x \rightarrow 4} f(x) exist when\[f(x)=\left\{\begin{array}{rcc}2 x+1 & \text { if } & 0 \leq x \leq 2 \\7-x & \text { if } & 2 \leq x \leq 4 \\x & \text { if } & 4 \leq x \leq 6\end{array}\right.\]

Example 7:Evaluate: \operatorname{Lim}_{\theta \rightarrow 0} \frac{1-\cos \theta}{\theta}
Example 7:Evaluate:  \operatorname{Lim}_{\theta \rightarrow 0} \frac{1-\cos \theta}{\theta}

Example7:Evaluate:Limθ01cosθθExample 7:Evaluate: \operatorname{Lim}_{\theta \rightarrow 0} \frac{1-\cos \theta}{\theta}

banner6000+ MCQs with instant video solutions