# Unit 01: Functions and Limits

Here is the list of important questions.

• Evaluate $\lim\limits_{\theta \to 0}\frac{1-\cos \theta}{\sin^3\theta}$ — FBSIC (2016)
• Graph the curve of the following parametric equations $x=\sec \theta$, $y=\tan\theta$ where $\theta$ is a parameter.— FBSIC (2016)
• Evaluate $\lim\limits_{x \to 2}\frac{\sqrt{x}-\sqrt{2}}{x-2}$ — BSIC Rawalpendi(2016), BSIC Rawalpendi(2017)
• Determine the function $f(x)=x^3+x$ as an even or odd function.— BSIC Rawalpendi(2017)
• Evaluate $\lim\limits_{\theta \to 0}\frac{\tan \theta-\sin \theta}{\sin^3\theta}$ — BSIC Rawalpendi(2017)
• Evaluate $f(x)=x^2-x$ then find $f(x-1)$ — BSIC Gujrawala (2017)
• $f(x)x^3-x$. Determine whether the $f(x)$ is even or odd. — BSIC Gujranwala (2017)
• Evaluate $\lim\limits_{x \to -1}\frac{x^3-1}{x+1}$ — BSIC Gujrawala (2017)
• Prove that $\lim\limits_{x \to 0}\frac{a^x-1}{x}=log_ea$ — BSIC Gujrawala (2017)
• Prove that $\cosh^2x-\sinh^2x=1$ — BSIC Rawalpindi(2016)
• Evaluate $\lim\limits_{x \to \pi}\frac{sinx}{\pi-x}$ — BSIC Rawalpindi(2016)
• Evalute $\lim\limits_{x \to 0}\frac{1-\cos2x}{x^2}$ — BSIC Rawalpindi(2016)
• Let the real valued functions $f$ and $g$ be defined by $f(x)=2x+1$ and $g(x)=x^2-1$. Obtain the exprssion for $fg(x);gf(x);f^2(x);g^2(x)$. — FBSIC (2017)
• Evalute $\lim\limits_{x \to 0}\frac{sinx^0}{x}$ — BSIC Gujranwala (2016)
• Evaluate $\lim\limits_{x \to 0}\frac{secx-cosx}{x}$ — BSIC Gujranwala (2016)
• Evalute $\lim\limits_{x \to \infty}\frac{2-3x}{\sqrt{3+4x^2}}$ — BSIC Gujranwala (2015)
• Prove that $\lim\limits_{x \to 0}\frac{a^x-1}{x}={log_e}^a$ — BSIC Gujranwala (2015)
• Find $f(x)$, if $f(x)=2+\sqrt{x-1}$. Also write domain and range of $f^{-1}(x)$ — BSIC Gujranwala (2015)
• Evaluate the limit. $\lim\limits_{x \to 0}\frac{\sec x- \cos x}{x}$ — BSIC Gujranwala (2015)
• Let the real valued functions $f$ and $g$ be defined by $f(x)=2x+1$ and $g(x)=x^2-1$. Obtain the expressions for $fg(x);gf(x);f^2(x);g^2(x)$ — FBSIC (2017)
• Evaluate $\lim\limits_{x \to 0}\frac{1-\cos p\theta}{1-\cos q\theta}$ — FBSIC (2017)
• Evaluate $\lim\limits_{x \to 3}\frac{x-3}{\sqrt{x}-\sqrt{3}}$ — BSIC Sargodha(2016)
• Determined the function is even or odd if $f(x)=x^3+x$.— BSIC Sargodha(2016)
• Define continuity of function at a point. — BSIC Sargodha(2016)
• $f(x)=(-x+9)^3$, find $f^{-1}(x)$ and verify $f(f^{-1}(x))=f^{-1}(f(x))=x$ — BSIC Sargodha(2016)
• Express the volume $V$ of a cube as a function of the area $A$ of its base. — BSIC Sargodha(2017)
• $f(x)=x^{\frac{2}{3}}+6$. Determine whether the $f(x)$ is even or odd. — BSIC Sargodha(2017)
• Evaluate $\lim\limits_{x \to -1}\frac{x^3+x^2}{x^2-1}$. — BSIC Sargodha(2017)
• Evaluate $\lim\limits_{\theta \to 0}\frac{\tan \theta -\sin \theta}{\sin^3 \theta}$. — BSIC Sargodha(2017)
• fsc-part2-ptb/important-questions/unit-01-functions-and-limits