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