In the limit #lim 16/x^4=oo# as #x->0#, how do you find #delta>0# such that whenever #0<absx<delta#, #16/x^4>10,000#?

Answer 1

Solve the inequality.

#16/abs(x)^4>10,000# is equivalent to
#16/(10,000) > abs(x)^4#

so

#abs(x) < root(4)(16/(10,000))# and
#absx < 2/10 = 0.2#
Let #delta = 0.2#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2
To find the value of delta, we need to solve the inequality 16/x^4 > 10,000. First, let's simplify the inequality by multiplying both sides by x^4: 16 > 10,000 * x^4 Next, divide both sides by 10,000: 16/10,000 > x^4 Simplify the left side: 0.0016 > x^4 Now, take the fourth root of both sides to isolate x: ∛(0.0016) > x Calculating the cube root of 0.0016, we find: ∛(0.0016) ≈ 0.040 Therefore, we can choose delta = 0.040 as a suitable value. Whenever 0 < |x| < 0.040, the inequality 16/x^4 > 10,000 will hold true.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7