66 Answered Questions for the topic limits of a function

I need a step-by-step solution for this limit

I need the limit of f(x)=(6sin(x )^2-sqrt(2)sin(x )-2)/(tan(x )-1) as x->π/4Please don’t use derivates, I haven’t studied them yet. The result should be 5/2, but I don’t know how to get it.... more

How do I solve these limit problems?

I need help solving these problems:Let g and h be the functions defined by g(x)=−2x^2+4x+1 and h(x)=(1/2)x^2−x+(11/2). If f is a function that satisfies g(x) ≤ f(x) ≤ h(x) for all x, what is lim... more

Calculus 1 Question

Let f(x)={(7x-9x^2 for x<0), (6x^2+7x for x>=0)}According to the definition of the derivative, to compute f'(0), we need to compute the left-hand limitlim x->0- ____________ which is... more

Compute f'(a) in two ways

f(x)=x3+2x a=1

Piecewise function limits

f(x)=( x2−x−6 /-5x3+15x2 ) x≠0, 3 2 x=0 -1/9 x=3Solve for the limit of f(x) as x approaches 0 from the leftSolve for the... more

Can someone help me with limits and absolute values please? :)

The instructions are to find the limit. My brain flipped upside down when seeing the absolute value symbols. lim |x-3| x-> 3- x2-7x+12Thank you!

Question regarding limits of sequences and functions.

Given that lim n→∞(1+1/n)^n = e :(a) Show that lim n→∞(1-1/n)^n = lim k→∞(k/k+1)^(k+1)(b) Hence, show that lim n→∞(1-1/n)^n = 1/e(c) Therefore, using the Squeeze Theorem, find lim n→∞(n!/n^n).

lim (n to inf) [ ln (1+3n+4n^2) - ln(5+6n+2n^2) ]

lim (n to inf) [ ln (1+3n+4n^2) - ln(5+6n+2n^2) ]My Friend and I have trouble on this questionwhat I do is this:lim (n to inf) [(1+3n+4n^2)/(5+6n+2n^2)] and then L'hopital's. the answer I got is... more

How do absolute sign works with functions?

If ƒ(x)=|x| then how is:ƒ(x)={x for x>0 -x for x<0 0 for x=0}Since absolute sign don't take negatives into consideration should'nt x<0 be also equal to x?

Find the limit (if it exists). lim x→0− x+8/cot x

I am confused as to how to find the limit for this questions as x approaches ) from the left. The cot portion is throwing me off a bit. Any help would be great! Cheers :)math

Consider the following limit. lim x→3 (x2 + 9) Find the limit L. Find δ > 0 such that |f(x) − L| < 0.01 whenever 0 < |x − c| < δ. (Round your answer to five decimal places.)

I understand how to find the limit, but I do not understand how to find the second portion. Any help would be great! Cheers :)

Limit of x*sin(1/x) as X approaches 0

After those steps, the result is wrong, and I can't understand what's wrong.lim(x→0) x·sin(1/x) =a = 1/xlim(x→0) x·sin(a)·a/a=lim(x→0) (x·sin(a)·a)/a=since lim(x→0) sin(a)/a = 1, than:lim(x→0)... more

Limits and derivatives

Limit n-> infinity ( sin^n 1 + cos ^n 1 ) ^n

How to know when to do certain steps to find the limit of an indeterminate form

For the functionf(x) = sqrt(x2 - 2) - sqrt(x2 - x)when taking the limit of x as it approaches infinity, if I use a conjugate first, and then divide the numerator and the denominator by the highest... more

Calculus please somebody help me with this!!

Let f(x)=(x)/(x+6). Find the values of x where f'(x)=5The greater solution is x=The lesser solution is x=

Calculus Limits

I am going crazy about this; can you please help and explain your answer lim y→5  1/y-1/5 ----------- y-5

Given f(x)=7/x, find the limit: lim h→0 [f(x+h)−f(x)]/h

I have zero clue how to do this...

Calculus (finding real value of X)

Find values of X, for which each function is continuousf(x)= (x-1) / (x^2+2x-3)

Evaluate the limit if f(x) = 8x on [0, 4].

lim N→∞ RN = ?

Limit x tends to 0 tan5 x/sinx

lim as x approaches infinity of the function (ln x^10000) /x

please help with question
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