Math Problem Statement

calculate the limit

Solution

To help you calculate the limit, please provide the specific limit expression you're working on.

For example, a limit can be written as: limxaf(x)\lim_{{x \to a}} f(x) or limxf(x)\lim_{{x \to \infty}} f(x)

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Here are 5 related limit questions for practice:

  1. Calculate limx0sinxx\lim_{{x \to 0}} \frac{\sin x}{x}.
  2. Calculate limx1x2\lim_{{x \to \infty}} \frac{1}{x^2}.
  3. Calculate limxexx2\lim_{{x \to \infty}} \frac{e^x}{x^2}.
  4. Calculate limx2x24x2\lim_{{x \to 2}} \frac{x^2 - 4}{x - 2}.
  5. Calculate limh0(3+h)29h\lim_{{h \to 0}} \frac{(3+h)^2 - 9}{h}.

Tip: If the direct substitution in the limit leads to an indeterminate form (like 0/00/0), try techniques such as factoring, L'Hopital's Rule, or simplifying the expression.

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Math Problem Analysis

Mathematical Concepts

Limits
Calculus
Indeterminate Forms

Formulas

Limit formula: \(\lim_{{x \to a}} f(x)\)
L'Hopital's Rule for indeterminate forms \(0/0\)

Theorems

L'Hopital's Rule
Squeeze Theorem
Limit definition of a derivative

Suitable Grade Level

Grades 11-12, College