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Exercise

$\lim_{x\to0}\left(\frac{hv}{e^v-1}\right)$

Step-by-step Solution

1

The limit of the product of a function and a constant is equal to the limit of the function, times the constant: $\displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}$

$h\lim_{x\to0}\left(\frac{v}{e^v-1}\right)$
2

The limit of a constant is just the constant

$h\frac{v}{e^v-1}$
3

Multiplying the fraction by $h$

$\frac{vh}{e^v-1}$

Final answer to the exercise

$\frac{vh}{e^v-1}$

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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$\lim_{x\to-4}\left(\frac{x+4}{x^2-16}\right)$

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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