# limit calc question

2 questions!!!

1.

Limit X approaching A

(X^1/3-a^1/3)/ x-a

2.
LiMIT x approaching 0
(1/3+x – 1/3) /x

On the first, would it help to write the denominator (x-a) as the difference of two cubes ((x^1/3 cubed - a^1/3 cubed)

second. use LHopitals rule. Take the derivative of the numerator, derivative of the denominator.

what if u never learned the lhopitals rule

All you have to do is to take the derivative of both numerator and denominator. That's L'Hopital's rule

If you never learned L'Hopital's rule, you should derive it first. Suppose that (a) = 0

Lim x--> a f(x)/g(x) =

Lim h--->0 f(a+h)/g(a+h) =

Lim h--->0
(f(a+h)- (a+h) - g(a)) =

Lim h--->0
[(f(a+h)- f(a))/h] /(g(a+h) - g(a))/h] =

The limit of a quotient is the quotient of the limits provided both limits exists and the quotient of the limits also exists.

1. 👍
2. 👎
3. 👁
1. 1. consider the question to look like this

lim (x^(1/3) - a^(1/3) ) / ( (x^1/3)^3 - (a^1/3)^3) as x ----> a

=lim (x^1/3 - a^1/3)/[ (x^1/3) - a^1/3)(x^(2/3) +x^1/3 a^1/3 + a^2/3) ] as x--->a
= lim 1/ (x^1/3) - a^1/3)(x^(2/3) +x^1/3 a^1/3 + a^2/3) as x --> a
= 1/(a^2/3 + a^1/3 a^1/3 + a^2/3)
= 1/(3 a^(2/3)

2. without L'Hopital's rule

lim (1/(3+x) - 1/3 )/x , as x-->0
= lim [(3 - 3 - x)/(3(3+x)) / x
= lim [ -x/(3(3+x))/x
= lim -1/(3(3+x)) as x-->0
= -1/9

1. 👍
2. 👎

## Similar Questions

1. ### Calculus

The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles. A = lim n → ∞ [f(x1)Δx + f(x2)Δx + . . . + f(xn)Δx] Use this definition to

2. ### Physics

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1500 kg and was approaching at 9.00 m/s due south. The second car has a mass of 700 kg and was approaching at 15.0 m/s due west. (a)

3. ### Calculus

Hi! My question is: Given that f is a function defined by f(x) = (2x - 2) / (x^2 +x - 2) a) For what values of x is f(x) discontinuous? b) At each point of discontinuity found in part a, determine whether f(x) has a limit and, if

A student in a parked car honks the horn, which has a `proper' frequency of 320 Hz. An observer in an approaching vehicle measures the frequency of the sound to be 355 Hz. Calculate the speed of the approaching vehicle. Use 340

1. ### Statistics

True or False According to the central limit theorem, the expected value for a sample mean becomes smaller, approaching zero, as the sample size approaches infinity.

2. ### Calculus Limits

Question: If lim(f(x)/x)=-5 as x approaches 0, then lim(x^2(f(-1/x^2))) as x approaches infinity is equal to (a) 5 (b) -5 (c) -infinity (d) 1/5 (e) none of these The answer key says (a) 5. So this is what I know: Since

3. ### Calc 1

The point (1,0) lies on the curve y=sin(10π/x). A) if Q is the point (x,sin(10π/x), find the slope of the secant line PQ. Points are 2,1.5,1.4,1.3,1.2,1.1,0.5,0.6,0.7,0.8,0.9 Do slopes appear to be approaching a limit? There is

4. ### Physics

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1200 kg and is approaching at 8.00 m/s due south. The second car has a mass of 850 kg and is approaching at 17.0 m/s due west. (a)

1. ### PHY1015S

A policeman in a stationary car measures the speed of approaching cars by means of an ultrasonic device that emits a sound with a frequency of 41.2 kHz. A car is approaching him at a speed of 33.0 m/s. The wave is reflected by the

2. ### Physics doppler effect

A person standing close to a railroad crossing hears the whistle of an approaching train. He notes that the pitch of the whistle drops as the train passes by and moves away from the crossing. The frequency of the approaching

3. ### physics

Approaching a flashing pedestrian activated traffic light, a driver must slow down to a speed of 30km/h. If the cross walk is 150m away and the vehicle's initial speed us 59km/h, what must be the magnitude of the car's

4. ### Calculus

Find the limit lim as x approaches (pi/2) e^(tanx) I have the answer to be zero: t = tanx lim as t approaches negative infi e^t = 0 Why is tan (pi/2) approaching negative infinity is my question?