Evaluate the Limit

Problem

(lim_t→∞)(√(,t+t2)/(4*t−t2))

Solution

1. Identify the highest power of t in the denominator to simplify the limit at infinity. The highest power is t2

2. Divide both the numerator and the denominator by t2 to normalize the expression.

(lim_t→∞)(√(,t+t2)/(t2)/(4*t−t2)/(t2))

3. Simplify the numerator by bringing t2 inside the square root as t4

(lim_t→∞)(√(,t/(t4)+(t2)/(t4))/((4*t)/(t2)−(t2)/(t2)))

4. Reduce the fractions inside the expression.

(lim_t→∞)(√(,1/(t3)+1/(t2))/(4/t−1))

5. Evaluate the limit by applying the property that (lim_t→∞)(1/(tn))=0 for n>0

√(,0+0)/(0−1)

6. Calculate the final numerical value.

0/(−1)=0

Final Answer

(lim_t→∞)(√(,t+t2)/(4*t−t2))=0

Want more problems? Check here!