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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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Final answer to the problem

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Step-by-step Solution

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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 differential calculus problems step by step online.

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

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Learn how to solve differential calculus 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: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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