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Exercise

$\lim_{x\to+0}\left(\frac{x^2\left(a^2-b^2\right)}{\cos ax-\cos bx}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to+0}\left(\frac{x^2\left(a^2-b^2\right)}{\cos\left(ax\right)-\cos\left(bx\right)}\right)$ by replacing all occurrences of $x$ by $+0$

$\frac{+0^2\left(a^2-b^2\right)}{\cos\left(+0a\right)-\cos\left(+0b\right)}$

Final answer to the exercise

$\frac{+0^2\left(a^2-b^2\right)}{\cos\left(+0a\right)-\cos\left(+0b\right)}$

Try other ways to solve this exercise

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  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

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