Limits Practice Problems

Limits in mathematics are defined as the values that a function approaches for given input values. Limits play a vital role in calculus and mathematical analysis and are used to define derivatives, integrals, and continuity.

Limits are unique real numbers. Let us consider a real-valued function “f” and the real number “p”, the limit is normally written as

Lim_x→p f(x) = L

It is read as “the limit of f of x, as x approaches p equals L”. The “lim” shows the limit and the fact that the function f(x) approaches the limit L as the right arrow describes x approaches p.

Limits Important Formulas

lim_x→0 (sin x) = 0

lim_x→0 (cos x) = 1

lim_x→0 ()= 1

lim_x→0 = 1

lim_x→0 log e^x = 0

lim_x→e log x = 1

lim_x→0 = 1

lim_x→0 = ln a

Limits: Practice Questions with Solution

Problem 1: Find the value of lim_x→0 x² + 1

Solution:

We have,

lim_x→0 x² + 1

Put x= 0 directly, we get value of limit as 1.

Problem 2: Check for the limit,

Solution:

Problem 3: Evaluate lim_x→3 ().

Solution:

Given

=

= x+3

lim _x→3 (x + 3) = 3 + 3 = 6.

Problem 4: Evaluate lim _x→∞

Solution:

Divide the numerator and the denominator by x³

lim _x→∞

= 5 − 0 + 0 / 1 + 0 + 0

= 5

Problem 5: Evaluate lim _x→0 tanx.

Solution:

lim_{x → 0} tan(x) = 0

Problem 6: Evaluate lim_x→2 (8 - 3x + 12x²).

Solution:

lim_x→2 (8 - 3x + 12x²)

= 8 - (3 x 2) + (12 x 4)

= 50

Related Articles:

• Limits, Continuity, and Differentiability
• Limit Formula

Limits Practice Problems: Unsolved

Problem 1: Evaluate lim_x→2 (3x - 5).

Problem 2: Evaluate lim _x→0.

Problem 3: Evaluate lim _x→1

Problem 4: Evaluate lim _x→∞

Problem 5: Evaluate lim _x→0 e^x - 1.

Problem 6: Evaluate lim _x→3

Problem 7: Evaluate lim _x→2 .

Problem 8: Evaluate lim _x→3 x - 3.

Problem 9: Evaluate lim _x→0 e^x.

Problem 10: Evaluate lim _x→3 x - 1.