Limits

Practice Questions with Step-by-Step Solutions Exponential Limits of the Form [\lim_{x \to 0} \left(\dfrac{1 + ax^2}{1 + bx^2}\right)^{\dfrac{1}{x^2}}] Standard Result…

1. Concept Overview In many algebraic limit problems, direct substitution leads to the indeterminate form [0/0]. Instead of factorisation or

1. Concept Overview: What Are Logarithmic Limits? A logarithmic limit is a limit in which the given expression involves a

Practice Questions with Step-by-Step Solutions Question 1. Evaluate: [\lim_{x \to 3} \dfrac{x^{2} − 9}{x − 3}] Step-by-Step Solution: Step 1:

1. Concept Overview: What Is L’Hospital’s Rule? L’Hospital’s Rule is a method used to evaluate limits of the form: [\dfrac{0}{0}]

1. Statement of the Concept (∞ / ∞ Form) When both the numerator and the denominator of a function tend

Practice Questions with Step-by-Step Solutions Question 1. Evaluate [\lim_{x \to 1} \dfrac{x^2 – 1}{x – 1}] Step-by-Step Solution: Step 1:

1. Introduction Trigonometrical limits are those limits in which trigonometric functions such as [sin x], [cos x], [tan x] appear,

Practice Questions with Step-by-Step Solutions Question 1. Evaluate: [\lim_{x→0} \dfrac{(\sin 5x)}{(3x)}] Step-by-Step Solution: As [x→0], we observe: [\sin 5x →

Practice Questions with Step-by-Step Solutions Question 1. Evaluate: [\lim_{x→0} \dfrac{(1-\cos 3x)}{(x^{2})}] Step-by-Step Solution: As [x→0]: [\cos 3x → 1] Hence,