Evaluate the limit using L'Hôpital's Rule, which states that if the limit of functions f(x) and g(x) as x approaches a point c are both 0 or both ±∞, then the limit of f(x)/g(x) as x approaches c is the same as the limit of their derivatives
step 2
Differentiate the numerator sin(x)−sin(tan(x)) and the denominator x2ln(1+x) with respect to x
step 3
Apply the derivatives and simplify to find the limit as x approaches 0
step 4
The result of the limit is −1/3, as obtained from the Asksia-LL calculator
Answer
limx→0x2ln(1+x)sinx−sin(tanx)=−31
Key Concept
L'Hôpital's Rule and Taylor Series Expansion
Explanation
The limit is evaluated using L'Hôpital's Rule, which involves taking the derivative of the numerator and the denominator. Additionally, the Taylor series expansion is used to express the functions around the point x=0 to find the limit.
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