Problem to solve
Compute \[ \lim_{ x \to \infty } \frac{2x+5}{x^2-7x+3} \]
Solution
STEP 1
Find the following limit:
lim_(x->∞) (2 x + 5)/(x^2 - 7 x + 3)
STEP 2
Hint: | Divide numerator and denominator of (2 x + 5)/(x^2 - 7 x + 3) by the denominator's leading term.
The leading term in the denominator of (2 x + 5)/(x^2 - 7 x + 3) is x^2. Divide the numerator and denominator by this:
lim_(x->∞) (2/x + 5/x^2)/(1 - 7/x + 3/x^2)
STEP 3
Hint: | Evaluate limits that tend to zero.
The expressions 5/x^2, 2/x, 3/x^2 and -7/x all tend to zero as x approaches ∞:
0
STEP 4
Hint: | Evaluate 0 1/1.
0 1/1 = 0:
Answer: | 
 | 0