Problem to solve
Compute \[ \lim_{ x \to -\infty } [3x^4-x^2+x-7] \]
Solution
STEP 1
Find the following limit: lim_(x->-∞)(3 x^4 - x^2 + x - 7)
STEP 2
Hint: | The limit of a polynomial at -∞ is the limit of its highest order term. lim_(x->-∞)(3 x^4 - x^2 + x - 7) = lim_(x->-∞) 3 x^4: lim_(x->-∞) 3 x^4
STEP 3
Hint: | If neither of the terms of a product approach 0 as x->a, then by the product rule, the limit of the product is the product of the limits. Applying the product rule, write lim_(x->-∞) 3 x^4 as 3 lim_(x->-∞) x^4: 3 lim_(x->-∞) x^4
STEP 4
Hint: | Apply the power rule. Using the power rule, write lim_(x->-∞) x^4 as (lim_(x->-∞) x)^4: 3 (lim_(x->-∞) x)^4
STEP 5
Hint: | As x approaches -∞, x approaches... lim_(x->-∞) x = -∞: 3 (-∞)^4
STEP 6
Hint: | Evaluate 3 ((-∞)^4). 3 ((-∞)^4) = ∞: Answer: | | ∞
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Edited by tododemate® - 2021