223 Answered Questions for the topic Limits

Limits Calculus

01/09/16

Let f(x)=(x^2)/1-x. Determine (limx->1+) xf(x)
how do I solve this? 
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01/09/16

Determine lim x->(infinity) 2^x +sin(x)
How do I solve this? The sine is really confusing me
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01/09/16

Determine Lim x->0 sin(3x^2)/x
How do I solve this?  I never learned how to solve limits with trig functions
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Limits

10/29/15

what is the limit (x->0) sin(x)/x
limits question.
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09/29/15

lim t?a (t^(2/3) - a^(2/3))/(t-a)
the original question is g(x)=t^(2/3) find g'(a) a≠0. I know how to find the derivative using the power rule, but I'm trying to help a Calc I student who hasn't started derivatives yet, and we're... more
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09/21/15

If a rock is thrown into the air on small planet with a velocity of 30 m/s, its height (in meters) after t seconds is given by y=30t-4.9t^2.
If a rock is thrown into the air on small planet with a velocity of 30 m/s, its height (in meters) after t seconds is given by y=30t-4.9t^2. Find the velocity of the rock when t=4. *You should... more
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09/21/15

Find the horizontal limit(s) of the following function: f(x)= (9x^3-8x^2-8x)/(7-8x-7x^3)
Find the horizontal limit(s) of the following function:   f(x)= (9x^3-8x^2-8x)/(7-8x-7x^3)   I know that one of the horizontal limits is the -9/7, but I'm still missing one and can't find it,... more
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09/16/15

can the product of two limits, one defined, the other DNE, be defined, or will it also be DNE?
Let's say you have: if lim x->a f(x) exists, lim x->a g(x) does not exist, could f(x)g(x) exist? By that same vein, if lim x->a f(x) exists, lim x->a g(x) does not exist, could... more
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09/07/15

List all vertical and horizontal asymptotes, if any, of f(x) and explain (using limits) why each is an asymptote.
Consider the function f(x) = [(x − 1)(x − 3)]/[2x(x+1)]   I think the vertical asymptotes are 0 and -1 and the horizontal asymptote is 1/2  please correct me if I am wrong...   I just need... more
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Limits Calculus

09/07/15

limits. with fractions in the numerator
lim x→0    (1/4)-(1/(x+4))         x   Step 1 would be to get common denominators on the top so....        (1/4)  - (1/(x+4))   =     1   -  1      = 1 (x+4)    -  1(4)         x            x... more
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Limits

08/26/15

limit and convergent
lim   (1/n+1 + 1/n+2 + ......... 1/2n) is equal to n→∞  a) 0  b) 1 c) 2 d) loge2 the answer is loge2 , bt howi cant understand, it should be zero i think, please solve it, plz plz  
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08/17/15

Limits help!!!
  Determine whether the function is continuous or discontinous. Justify your reasoning. If discontinuous, identify points of discontinuity.                   2-X^2 if X <= 1 ƒ(x)=... more
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Limits

08/11/15

calculus question
lim h(t), where h(t)= (cos(t)-1)/(t^2). note that h(t) is even, that is, h(t)=h(-t). t--0   t=  (+-)0.002   (+-)0.0001   (+-)0.00005   (+-)0.00001   My answers.. h(t)= .4999          ... more
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08/05/15

What is the smallest value of a if the area under the curve y=e^(ax) from -infinity to 4 is 11?
What is the smallest value of a if the area under the curve y=e^(ax) from -infinity to 4 is 11? I cannot seem to arrive at the answer using integrals. Please help.
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Limits

07/22/15

What is lim ([|x|] - x)/(3-x) as x approaches 3 from the left? Please include the process of solving. Thank you.
It is one of the items in my problem set.  I am enroled at a distance learning program and I see my professor rarely. I hope someone could help.
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Limits

06/20/15

Limits Question (dividing by zero?)
Calculate: lim x->0 (sin4x2)/(x2)   I've seen an explanation of the problem and it says the answer is 4. I just don't understand what you're supposed to do after u-substitution. More... more
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05/07/15

Show that when r changes by ?r; the change in the acceleration due to gravity, g; is given by ?g ˜ -2g ( ?r / r)
The acceleration due to gravity, g; is given byg = GM / r2 ; where M is the mass of the earth, r is the distance from the center of the earth,and G is the universal gravitational constant. Show... more
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05/06/15

show the derivatives of the quotient
The de?finitions of derivative of two functions f and g are given by:f' (x) = lim     f(x + Δx) - f (x) / Δx , g'(x) = lim   g(x + Δx) - g(x) / Δx           x->0                              ... more
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Limits Calculus 1

04/01/15

find the limit
lim  (ln(x^-1))^x x->0+
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02/19/15

Given that f'(x)=lnx evaluate the limit as h approaches 0 (f(2+h)-f(2))/h
Please explain how to do this 
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02/17/15

Trigonometric limits Please help!
lim (x--> p/3) sin(x-3)/(4cos2-1)
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02/15/15

Limits of sequences, please help!
limn->infinite[ (-1)n/(n3-12)}  I dont know what to do with (-1)n, if it's equal to infinite then if I divide by n3, it's infinite over infinite. I dont understand :S. And the question is if... more
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Limits

02/15/15

Evaluate the limits
Evaluate lim ((x^(1/n)-a^(1/n))/(x-a)) as x->a and lim ((x^n-a^n)/(x-a)) as x->a?   I didnt learn l'hopital's rule  
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Limits

02/15/15

Evaluate: lim ((x^(1/3)-a^(1/3))/(x-a)) as x->a
How to get 1/3a^(2/3)
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Limits

02/09/15

find the limit
lim       (8)/(xcot5x)=? x→0  
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