List of practice Questions

Evaluate \(\lim_{x\rightarrow 5}\) f(x), where f(x) = |x|-5

Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \(\frac{cos\,x}{\pi-x}\)

Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \(\frac{cos^2x-1}{cos\,x-1}\)

Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \(\frac{ax+xcos\,x}{b\,sin\,x}\)

Evaluate the Given limit: \(\lim_{x\rightarrow 0} x\,sec\,x\)

Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) sinax =\(\frac{bx}{ax}\)+ sinbx a,b,a+b ≠ 0

Evaluate the Given limit: \(\lim_{x\rightarrow 0}(cosec\,x-cot\,x)\)

Evaluate the Given limit: \(\lim_{x\rightarrow \frac{\pi}{2}}\frac{tan\,2x}{x}-\frac{\pi}{2}\)

Find \(\lim_{x\rightarrow 0}\) f(x) and \(\lim_{x\rightarrow 1}\) f(x) where { 2x+3, x≤0 3 (x+1), x>0

Find \(\lim_{x\rightarrow 1}\) f(x) where { x² -1, x≤1 -x²-1, x>1

Evaluate \(\lim_{x\rightarrow 0}\)f(x), where { |x|/x, x≠0 0, x=0

Evaluate \(\lim_{x\rightarrow 0}\) f(x), where { \(\frac{x}{|x|}\), x≠0 0, x=0

Suppose f(x) ={ a+bx, x\(<\)1 4, x=1 b-ax x\(>\)1 and if lim x \(\rightarrow\)1 f(x) = f(1), what are possible values of a and b?

Let a₁, a₂,..., a_n be fixed real numbers and define a function f(x)=(x-a₁)(x-a₂)...(x-a_n).
What is \(\lim_{x\rightarrow a_1}\) f(x)? 
For some a ≠ a₁, a₂ .....a_n, Compute \(\lim_{x\rightarrow a}\) f(x).

If f(x)={|x|+1, x <0 0, x=0 |x|-1, x>0}
For what value (s) of a does lim x\(\rightarrow\)af(x) exist?

If the function f(x) satisfies \(\lim_{x\rightarrow 1}\) \(\frac{f(x)-2}{x^2-1}\) =\(\pi\), evaluate \(\lim_{x\rightarrow 1}\) f(x).

If f(x) = \(f(x)=\left\{\begin{matrix} mx^2+n, &\,\,\,\,x<0 \\   nx+m,&\,\,\,\, 0\leq x\leq1 \\   nx^3+m,&\,\,\,\, x>1  \end{matrix}\right.\). For what integers m and n does both \(\lim_{x\rightarrow 1}\)f(x) and \(\lim_{x\rightarrow 1}\) f(x) exist?

Evaluate the Given limit: \(\lim_{x\rightarrow \pi}\)(x - \(\frac{22}7{}\))

Evaluate the Given limit: \(\lim_{x\rightarrow 1}\pi r^2\)

Evaluate the Given limit: \(\lim_{x\rightarrow 1}4\) \(\frac{4x-3}{x-2}\)

Evaluate the Given limit: \(\lim_{x\rightarrow -1}\) \(\frac{x^{10}+x^5+1}{x-1}\)

Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \((x+1)^5-\frac{1}{x}\)

Evaluate the Given limit: \(\lim_{x\rightarrow 2}\) \(\frac{3x^2-x-10}{x^2-4}\)

Evaluate the Given limit: \(\lim_{x\rightarrow 3}\) \(\frac{x^4-81}{2x^2-5x-3}\)

Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \(\frac{ax+b}{cx}\) + 1