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Find the limit of $\frac{\frac{1}{x+1}+\frac{-1}{\sqrt{1-x^2}}}{2x}$ as $x$ approaches 0

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Solution

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Final answer to the problem

indeterminate

Step-by-step Solution

How should I solve this problem?

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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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The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors

Learn how to solve limits by direct substitution problems step by step online.

$L.C.M.=\left(x+1\right)\sqrt{1-x^2}$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit of (1/(x+1)+-1/((1-x^2)^(1/2)))/(2x) as x approaches 0. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors. Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete. Simplify the numerators. Combine and simplify all terms in the same fraction with common denominator \left(x+1\right)\sqrt{1-x^2}.

Final answer to the problem

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Function Plot

Plotting: $\frac{\frac{1}{x+1}+\frac{-1}{\sqrt{1-x^2}}}{2x}$

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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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