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- Solve using L'H么pital's rule
- Solve without using l'H么pital
- 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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Change the logarithm to base $e$ applying the change of base formula for logarithms: $\log_b(a)=\frac{\log_x(a)}{\log_x(b)}$
Learn how to solve limits by direct substitution problems step by step online.
$\lim_{x\to0}\left(\frac{\frac{\ln\left(\cos\left(2x\right)\right)}{\ln\left(10\right)}}{7x^2}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit of log(cos(2*x))/(7x^2) as x approaches 0. Change the logarithm to base e applying the change of base formula for logarithms: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. Divide fractions \frac{\frac{\ln\left(\cos\left(2x\right)\right)}{\ln\left(10\right)}}{7x^2} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. If we directly evaluate the limit \lim_{x\to 0}\left(\frac{\ln\left(\cos\left(2x\right)\right)}{7\ln\left(10\right)x^2}\right) as x tends to 0, we can see that it gives us an indeterminate form. We can solve this limit by applying L'H么pital's rule, which consists of calculating the derivative of both the numerator and the denominator separately.