Important questions FSc part 2 unit 1 Functions and Limits

 

Unit 01: Functions and Limits

Here is the list of important questions.

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