29 Answered Questions for the topic Limits And Derivatives

06/03/18

#### Limits at infinity

i am confused, we should divide the whole fractions by the greatest power right?

03/13/18

#### How can I transform −λ△t= (N(t+△t)−N(t)) / (△t) into the formula dN/dt=−λN using limits?

How can I transform −λ△t= (N(t+△t)−N(t)) / (△t) into the formula dN/dt=−λN using limits? This is in relation to radioactive decay for those that are wondering, thank you for your help and time!...
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03/01/18

#### Find each limit by evaluating the derivative of the function

Find each limit by evaluating the derivative of the function
limh→0 ((3(2+h)2-(2+h)-10))/h

01/27/18

#### Use limits to compute the derivative

Use limits to compute the derivative.
f'(4) if f(x)=5x3

01/09/18

#### An object is thrown downward from the top of a building. After 𝑡 seconds, the object’s height (in feet above the ground) is given by the formula 𝑠(𝑡)=−16𝑡2

An object is thrown downward from the top of a building. After 𝑡 seconds, the object’s height (in feet above the ground) is given by the formula 𝑠(𝑡)=−16𝑡2−30𝑡+190. a) Determine the object’s...
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01/01/18

#### Find derivative of cosx at x=0

Using the formula, derivative of f at point a is denoted by f'(a), f'(a)=Lim(h→0) (f(a+h)-f(a)) /h

11/11/17

#### 3x^3-10x^2+7x-12 How to Factor, please help asap. T_T

3x^3-10x^2+7x-12 How to factor. with x-3 on it. Please help. Thank you! You are a life saver.

11/10/17

#### f(x) = 3√ x · sin x use the definition of derivative to show f(x) is differentiable at x=0

this question had several parts
1)Why can't we use the product rule to compute f'(0)
My initial thought was that you cannot use the product rule t because sinx and 3√ x both equal 0 at...
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12/28/16

#### Finding critical points and limits.

Let f(x,y) = 1/(x2 - y)
(a) Determine the critical points of f.(b) Does the limit of the function f at the point (0, 0) exist? Justify your answer

10/13/16

#### limit of sin(x)/x as x approaches infinity

I believe it equls 1, but how? I tried L'Hopital's Rule and still can not get just a Cos(x) as x approaches infinity

09/19/16

#### How to find the limit process to find the area of the region

How to find the limit process to find the area of the region between f(x)=1/10(x^2+10x) and the x axis on the interval [1,10]

06/18/16

#### evaluate lim x ->infinite 1.2+2.3+3.4+..+n(n+1)/n3

i couldnt get the answer cause i dont know the value of sigma n(n+1)

04/22/16

#### PROFIT FUNCTION IN CALC

I need help answering this word problem...I need to find the function P(t) and I just can't remember the process whatsoever
"A company has its profit function P(t) defined since its inception...
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01/16/16

#### Suppose limh->0 (f(h)-f(0))/h =+infinity and f(0)=0. What kind of feature can best explain this?

a)such scenario is not possible
b)f(x) has a vertical tangent at x=0
c)f(x) must be discontinuous at x=0
d)f(x) has a vertical assymptote at x=0, and f(0) is defined to be 0.
I tried a) and...
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01/16/16

#### The expression f(a+h)-f(a)/h is called the

a)instantaneous rate of change of f at a
b) difference quotient of f at a
c)definition of f'(a)
d)secant line of f at a
I tried a) and c) but they're wrong.
What is it supposed to be?

10/05/15

#### Use the Intermediate Value Theroem to solve

A monk leaves the monastery at 7:00 am and takes his usual path to the top of the mountain, arriving at 7:00 pm. the following morning, he starts at 7:00 am at the top and takes the same path back...
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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...
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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...
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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 ...
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04/19/15

#### Find the derivative of the following functions: d^2 / dx2 (x sin x)

Find the derivative of the following functions: d^2 / dx2 (x sin x)

04/19/15

#### Use linear approximation and differential to approximate: sin 31`

Use linear approximation and differential to approximate: sin 31`

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