Limits at infinity Questions and Solutions

In some questions, the limits should be calculated when the value of variable tends to infinity. So, it is essential for students to learn how to find the limits as the variable of function approaches infinity. The limits as the value of variable approaches infinity worksheet with examples is given for your practice with answers, and also solutions for you to learn how to find the limits as the variable tends to infinity by using the infinite limits rules in possible methods.

Algebraic functions

$(1).\,\,$ Evaluate $\displaystyle \large \lim_{x\,\to\,\infty}{\normalsize \bigg(2+\dfrac{3}{x^2}\bigg)}$

$(2).\,\,$ Evaluate $\displaystyle \large \lim_{x\,\to\,\infty}{\normalsize \dfrac{\sqrt{3x^2-1}-\sqrt{2x^2-1}}{4x+3}}$

$(3).\,\,$ Evaluate $\displaystyle \large \lim_{x\,\to\,\infty}{\normalsize \bigg(\dfrac{x^3}{2x^2-1}+\dfrac{x^2}{2x+1}\bigg)}$

Trigonometric functions

Evaluate $\displaystyle \large \lim_{x\,\to\,\infty}{\normalsize x\sin{\bigg(\dfrac{1}{x}\bigg)}}$

Logarithmic functions

Exponential functions

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