How Do You Solve These Challenging Calculus Limit Problems?

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In summary, the conversation discusses several limit questions, including a cubed root problem, a binomial expansion problem, and an absolute value problem. The first problem is solved to be 2/3. The binomial expansion problem is solved using a binomial expansion of (1+x)^1/2. The absolute value problem is solved by graphing and finding the limit to be 0, and r(0) to be 0.
  • #1
venom2121
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few calc limit questions! need help!

Homework Statement



limit x-> -1 of cubed rt (3x-5/25x-2)
not sure how to go about this at all

i think the answer is 2/3 but i can't work it up


lim x->0 √(3x+2) - √2
x


r(x)= |3x| A) lim x->0 of r(x) question 2 B) r(0)
x





The Attempt at a Solution

 
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  • #2


these weren't formatted right. the middle one the x is underneath the top term as well as for the absolute (|3x|)/x

also, i tried to multiply the middle one by its conjugate √(3x+2) - √2

i wind up getting (3x)/(x (√(3x+2) - √2) ) i think that's the right track but I am not sure
 
  • #3
welcome to pf!

hi venom2121! welcome to pf! :smile:

(btw, never reply to your own first post :redface:, use the EDIT button instead … then you'll stay on the No-replies list! :wink:)
venom2121 said:
limit x-> -1 of cubed rt (3x-5/25x-2)
not sure how to go about this at all

i think the answer is 2/3 but i can't work it up

but it isn't 0/0, so what's the difficulty? :confused:

just put x = -1 ! :rolleyes:
lim x->0 (√(3x+2) - √2)/x

use a binomial expansion (and √(3x+2) = √x√(3 + 2/x)) :wink:
r(x)= (|3x|)/x

try drawing a graph :wink:
 
  • #4


the cubed rt problem the answer is supposed to be 2/3 DERP ok had a brain fart haha got that now..

im still confused about the binomial expansion. and as far as the absolute value one I am not sure. i see that the y values max out at -3 and 3 and as it goes to zero the y values stay at 3 until zero. so is that the limit? would that mean that r(0)=0? also how would you figure this out without graphing?
 

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  • #5
venom2121 said:
im still confused about the binomial expansion.

can't you do the binomial expansion of (1 + x)1/2 ?
and as far as the absolute value one I am not sure. i see that the y values max out at -3 and 3 and as it goes to zero the y values stay at 3 until zero. so is that the limit? would that mean that r(0)=0?

not following you :confused:
also how would you figure this out without graphing?

i wouldn't!
 
  • #6


venom2121 said:

Homework Statement



limit x-> -1 of cubed rt (3x-5/25x-2)
not sure how to go about this at all

i think the answer is 2/3 but i can't work it up


lim x->0 √(3x+2) - √2
x


r(x)= |3x| A) lim x->0 of r(x) question 2 B) r(0)
x





The Attempt at a Solution


Your "cube-root" problem, as written, is
[tex] \lim_{x \rightarrow -1} \sqrt[3]{\left( 3x - \frac{5}{25x} - 2\right)} = -\frac{\sqrt[3]{600}}{5},[/tex]
but perhaps you meant
[tex] \lim_{x \rightarrow -1} \sqrt[3]{\left( \frac{3x-5}{25x - 2}\right)}.[/tex]
In that case you should have used brackets, and written cube rt ((3x-5)/(25x-2)).

RGV
 

FAQ: How Do You Solve These Challenging Calculus Limit Problems?

What is a limit in calculus?

A limit in calculus is a fundamental concept that describes the behavior of a function as the input value approaches a particular value. It represents the value that the function is approaching, rather than the value that it is actually equal to at that point.

How do you find the limit of a function?

The limit of a function can be found by evaluating the function at values close to the given input value and observing the trend of the output values. This can be done analytically using algebraic techniques or graphically by plotting the function and observing its behavior as the input value approaches the desired value.

What is the difference between a one-sided limit and a two-sided limit?

A one-sided limit only considers the behavior of the function as the input value approaches from one direction (either from the left or the right), while a two-sided limit takes into account the behavior from both directions. One-sided limits can be used to determine if a function is continuous at a particular point, while two-sided limits are necessary for determining the existence of the limit.

What is the limit of a constant function?

The limit of a constant function is equal to the value of the constant. This is because the function remains constant regardless of the input value, so the limit as the input value approaches any value is the same as the value of the function at that point.

How can limits be used in real-life applications?

Limits are used in various fields such as physics, engineering, and economics to model and predict real-life situations. For example, the concept of a limit is crucial in determining the maximum velocity of an object, the optimal production level for a business, or the population growth rate of a species. It also plays a role in understanding and solving optimization problems in various industries.

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