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Category: Calculus

L’Hôpital’s rule

Evaluating the limit of x-3 with x approaching 4 is very easy and straightforward: you just plug in the value x tends to and you’re done! Another example: How about this? As we saw here, one divided by zero equals infinity, therefore one divided by infinity equals zero. We can’t evaluate limits directly by substitution when, if we do substitute, we get an indeterminate result, like infinity/infinity, 0/0, infinity – infinity, 0 times infinity, infinity/0. When this happens, we need to rewrite the limit, without substitution, and apply L’Hôpital’s rule.… Read more L’Hôpital’s rule

How to solve definite integrals

Indefinite integrals are used to find the formula for the area under a curve of function f(x), whereas definite integrals allow you to calculate the value of the area. It’s like the area of a rectangle, b*h: this is the formula, and in order to find the value you have to plug in the values of b and h. The same is for definite integrals. A definite integral is generally written like this: where a and b are called respectively lower and upper bounds. Also, As you can see, if… Read more How to solve definite integrals