29 Answered Questions for the topic Limits And Derivatives

Limits at infinity

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

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!... more

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

Use limits to compute the derivative

Use limits to compute the derivative    f'(5) f(x)=7x3

Use limits to compute the derivative

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

Use limits to compute the derivative

Use limits to find the derivative   f'(2) if f(x)=4x3

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... more

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

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.

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... more

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

calculus limits

lim x → ∞  √(4x2-2x+5)  / (3x+7)

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

(tanx+sqrt(3))/(x-2pi/3)

What is the limit as x approaches 2pi/3.

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]

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)

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... more

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... more

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?

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... more

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

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

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

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)

Use linear approximation and differential to approximate: sin 31`

Use linear approximation and differential to approximate: sin 31`
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