Evaluate the Limit

Problem

(lim_x→0)(sin(11*x)/(8*x))

Solution

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

2. Recall the fundamental trigonometric limit identity:

(lim_θ→0)(sin(θ)/θ)=1

3. Rewrite the expression to match the identity by factoring out the constant 1/8 from the denominator:

1/8⋅(lim_x→0)(sin(11*x)/x)

4. Manipulate the expression to create the argument 11*x in the denominator by multiplying the numerator and denominator by 11

11/8⋅(lim_x→0)(sin(11*x)/(11*x))

5. Apply the limit identity where θ=11*x As x→0 it follows that 11*x→0

11/8⋅1=11/8

Final Answer

(lim_x→0)(sin(11*x)/(8*x))=11/8

Want more problems? Check here!