Evaluate the Limit

Problem

(lim_x→0)((x3+12*x2−5*x)/(5*x))

Solution

1. Identify the indeterminate form by substituting x=0 into the expression, which results in 0/0

2. Factor out the common factor of x from each term in the numerator.

(x*(x2+12*x−5))/(5*x)

3. Simplify the expression by canceling the common factor of x from the numerator and the denominator, assuming x≠0

(x2+12*x−5)/5

4. Evaluate the limit by substituting x=0 into the simplified expression.

(0+12*(0)−5)/5

5. Calculate the final numerical value.

(−5)/5=−1

Final Answer

(lim_x→0)((x3+12*x2−5*x)/(5*x))=−1

Want more problems? Check here!