Finding Limits

In Exercises ...

Question

Finding Limits

In Exercises 25–28, find the limit of g(x) as x approaches the indicated value.

lim (4g(x))¹/³ = 2

x →0

Accepted Answer

Welcome back, everyone. Calculate the limit of H X as X approaches -2, given that limit as X approaches -2 of 2 H X to the power of 1/4 equals 4. We're given 4 answer choices A says 128, B 64, C 32, and D 256. So first of all, what we're going to do is analyze the given limit. It says limit. As x approaches -2 of 2 H of X, raise to the power of 1/4 equals 4. Now, what we can do is basically recall that, according to the properties of limits, we can rewrite that exponent for the whole limit. So we can write it as limit. As x approaches -2 of 2 H of X, and now our limit is raised to the power of 1/4, and this gives us 4, right? So we're applying the properties of exponents or the limit. What we can do now is basically extract the limit itself, and we can do that by raising both sides to the power of 4, right? We can raise 4 to the power of 4, and we can raise the left hand side to the power of 4. Right, because 4 multiplied by 1/4 will give us 1, and this means that limit. As x approaches -2 of 2 H of X is equal to 4 the power of 4, which is 256, and now because we have a constant, we can basically factor it out. This is another property of limits. It essentially says that if we have a constant in front of our function, it has no effect for the calculations so we can just factor it out in front of the limit. This means that 2 multiplied by limit as x approaches -2 of each of X. is equal to 256 and now you can see that we will be able to get the value that we want, right? We want to calculate the limit as X approaches -2 of H of X. We can do that by dividing both sides by 2. So limit As X approaches -2 of H of X is simply 256 divided by 2. Which is equal to 128. This means that the final answer to this problem corresponds to the answer choice A. Thank you for watching.

Finding Limits

In Exercises 25–28, find the limit of g(x) as x approaches the indicated value.

lim (4g(x))¹/³ = 2
x →0

Watch next

Finding LimitsIn Exercises 25–28, find the limit of g(x) as x approaches the indicated value.lim (4g(x))¹/³ = 2x →0

Watch next

Finding Limits

In Exercises 25–28, find the limit of g(x) as x approaches the indicated value.

lim (4g(x))¹/³ = 2
x →0