Maths Calculus Derivatives & Limits

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Maths Calculus Derivatives & Limits

Using the definition of the derivative evaluate the following limits 1) Lim h---> 0 [ ( 8 + h )^1/3 - 2 ] / h 2) Lim x ---> pi/3 ( 2cosx - 1 ) / ( 3x - pi)

Calculus (Derivatives)

What is the derivative of the this functon? g(x) = -500/x, x cannot equal 0. I know that in order to fnd the derivative I need to put the function into the equation for evaluating derivatives as limits. lim as h -> 0 (f(x+h) - f(x))/h I did this, but I am having ...


Apply the concepts of calculus (limits and derivatives) to describe the graph y = sec(x). Include a quality graph

Calculus: Derivatives

I'm having trouble understanding what derivatives in calculus (instantaneous speed) is. Can someone please explain it to me, or provide some easy links to learn from? Thanks!


We are doing limits in Calculus, but now we are doing trig limits too and i do not get how to do any of them. For example ones like this, how do you do them? sec (x-1) / (x sec x) x approaches 0 ((3 sin (x)) 1 - cos(x)) / (x^2) x approaches 0 (sin (2x)) / (sin (3x)) x ...


find the second-order partial derivatives of f(x,y)=x^3 + x^2y^2 + y^3 + x+y and show that the mixed partial derivatives fxy and fyx are equal

Math - Calculus 1

Approximate using derivatives. (Must show work using derivatives!) Do not use a calculator: (1.1)^4 - (1.1)^2

calculus (limits)

Use limits to explain why f(x)= (7-3X)/(X+9) has a vertical asymptote.

Math - Limits/Derivatives

The demand x is the number of items that can be sold at a price of $p. For x = p^3 - 4p + 400, find the rate of change of p with respect to x by differentiating implicitly.

calculus - derivatives

can you please find the first 5 derivatives for: f(x) = (0.5e^x)-(0.5e^-x) f'(x) = ? f''(x) = ? f'''(x) = ? f''''(x) = ? f'''''(x) = ? thanks :) f(x) = (0.5e^x)-(0.5e^-x) f'(x) = 0.5 e^x + 0.5 e^-x f''(x) = 0.5 e^x - 0.5 e^-x f'''(x) = 0.5 e^x + 0.5 e^-x f''''(x) = 0.5 e^x - 0...

convert derivatives of x,y,z, to r, Ɵ,z

convert derivatives of x,y,z, to r, Ɵ,z with chain rule? I want provment rules of converting rectangular derivatives to cylindrical derivatives and and also cylindrical to spherical.I know the rules but I cant prove EQUATIONS.thx alot


I studied derivatives before, but kind of forgot them all, is there a website that gives me an overview of derivatives. What is first and second derivatives, how to find it, all the derivative rules and so on... thank you

Maths (limits)

how do i evaluated these limits: lim x --> 3 ((square root of x^2 +16)- 5)/(x^2 - 3x) lim x--> to infinity (2+ 100/x)


TWO examples of each of the following: two sided limits and theorem on limits (SUM, difference, product, quotient, nth root, ).


I'm in Calculus AP and we are learning about limits. I'm having trouble with finding limits algebraically. So here's a sample that you can use to help explain this to me. Find the limit of lim x (arrow to the right) 1 x-1/x(squared)-1. Please help!

AP Calculus

Find each of the limits without a calculator. Use the limits as an aide to sketch the graph of f(x)= (x-2)/(|x|-2) for-10<_x<_10 and -6<_y<_6. Be sure to clearly indicate any asymptotes, holes or other important characteristics. lim x->∞ f(x)


In addition, can you walk me through how to get the derivatives for these 2 statements, too? a) y = x^5/3 - 5x^2/3 b) y = (the cubed root of the quantity) [(x^2 - 1)^2] Hi there. I need to find the first derivative of this statement. y=x(x+2)^3 I tried the chain rule, but I ...


TWO examples of two sided limits and each theorem on limits.

Maths Derivatives

If y = x ^ n + ( 1 / x ^ n ) prove that ( x^2y'' ) + ( xy' ) - ( n^2y ) = 0

Calculus please help!!! double integral

Combine the following two integrals into one by sketching the region, then switching the order of integration. (sketch the region) im gonna use the S for integral sign..because idk what else to use. SS6ycos(x^3-3x)dxdy+SS6ycos(x^3-3x) And the first integration limits for x are...

Calculus grade 12

a) determine the derivative of y = sin2x b) determine the derivative of y = 2SinxCosx c) shoe that derivatives in parts a) and b) are equal d) explain why derivatives in parts a) and be should be equal.


Find the outside and inside functions of the following to find their derivatives: 1) sqrt(2x+9) 2) cos(cos(x)) 3) tan(x) I already know how to find their derivatives I'm just not exactly sure what parts of the chain rule equation would be considered the outside and inside.


Applications of derivatives A rectangle has its base on the x axis and its upper two vertices on the parabola y=12 - x^2. What is the largest area the rectangle can have, and what are its dimensions. Support your answer graphically. Thanks. Well, the parabola is symettric ...


Find the derivatives of these: f(x)=√


show that the curves r=asin(è) and r=acos(è) intersect at right angles. can you show that the derivatives for each are the negative reciprocal of each other? That is the key. i need more info..i know how to find the derivative...but how will that prove my question. Do I need...


derivatives. f(x)=(1/-7x^12) f'(2)=? f'(-1)=?

Derivatives ~ Calculus

If dy/dx = (1 + x)/(xy), x>0, and y=-4 when x=1, then when x=3, y= what?

math (Calculus III)

In this example we should use the beta function. But I'm a bit lost, because I don't know how to change the limits of the integral to fit the one that is needed when using B-function. The problem goes like this: integrate cos^7(x) dx, limits of the integral are from 0 to pi.


a)find the first partial derivatives of f(x y)= x √1+y^2 b)find the first partial derivatives of f(x,y)= e^x ln y at the point (0,e)


Compute the derivatives of : f(x)= x^7 + 7^x+ 7^7


Determine h'(x) for h(x)= [x/(1-x)]^2


Anti-Derivatives 2x^6-x^3/x^2


if f(x)=x^3+5x, then f'(2)= if f(x)=cos(2x), then f'(pi/4) derivatives and anti derivatives please help


find the derivatives F(x)=8ln(x^5-2x)

calculus derivatives

Please confirm: {(5x+2)^4/x^2-3x+1)^3}= 20(5x+2)^2(x^2-3x+1)^3 -3x^2(5x+2)^4 (x^2-3x+1)^2/(x^2-3x+1)^6


Find the derivatives of the functions k(x)=(x^3+e^x)^4

Calculus (derivatives)

Find the derivative of cos^2(4x)


find the derivatives 1. y=sin^3(2x)(cos2x)


find the derivatives 1. y=sin^3(2x)(cos2x)


derivatives: 2. cos teta/ 1+sin^2


Find the derivatives of the following function: i)y=-3x^-3 +2x^-2 + x-2


find the maximum valu of any of the function without using derivatives 16x+8x+7


Just got through with derivatives, power rule, and chain rule. I am supposed to find the first and second derivatives of the function. y = 4x/√x+1 and y = cos^2(x) y' = [(x+1)^(1/2)(4)]-[(4x)(1/2(x+1)^(-1/2))(1)] y' = [4(x+1)^(1/2)-4x]/[2(x+1)^(1/2)(x+1)] y' = (2-4x)/(x+...

Maths Calculus

We want to build a rectangular cardboard box with no top and of given volume V using the least quantity of cardboard. Find the length of the box's edges by fnding the minimum of the total surface function. Verify that the point you found is indeed a minimum applying the second...


Find a formula for the derivatives of the function m(x)=1/(x+1) IS the answer -1/(x+h)(x+h+1)


derivatives: 3. y= cot^3(2/x) 4. y= csc^5 (1-t+3t^2) 5. y=sec(5x)/tan3x


f(x)=7cosx+6tanx, find f'(x)and f'(5pie/4)

Calculus (derivatives)

find the slopes at the indicated points y = 3 + 5x - 3x^3 (0,3), (1/2, 41/8), (2,-11)


Z=square root of(x^2+y^2) + xy Find the partial derivatives: x, xx, y, yy, xy. Thanks.


I get mixed up when graphing derivatives. If I'm given the graph of f how do I get f' and f"?

Calculus, derivatives

The curve is given by x^2+2r(sqrt(y))=xy What is dx/dr when y is constant?

Calculus, derivatives

Derivative of y=(a^x)+(x^a). Show steps, please.


find the first and second derivatives for 3x^4-4xy^2+7=2y

maths, limits

lim of x to 0 = x^2+1


Find the first and second derivatives of the function. h(x) = sqrt x^2 + 1


find the partial derivatives du/dx, du/dy and du/dt. u= root (r^2+s^2, r = y + x cos(t), s = x + y sin(t);when x = 0, y = 2, t = 2


f(x) = (x-1)^(2/3)*(x+3) What are the critical numbers? the derivative would be =2/3(x-1)^(-1/3)(x+3) + (x-1)^2/3 What do I do next?


Find all first partial derivatives: f(x,y)=e^(xy)cosx


At what points on the graph of f(x)=6x^2+4x-9 is the slope of the tangent line -2?

Calculus - Anti-Derivatives

How would you find the Integral of (cos(x\8))^3, defined from -(4 x pi)/3) to (4 x pi)/3)

calculus - (derivatives)

Find the derivative of the function f by using the rules of differentiation. F(x) = 3 ã x

Calculus First Derivatives

If f(2) = 2.5 and f'(2) = -2.5, then f(2.5) is approximately... I have no idea how to do this without an equation.


I need to find the derivative and can't do them when they are raised to powers? Thank You. m(x)x^5 - 5x^3+7x -4)^10 (4x^9 +19)^23 this on is tuff!

Calculus - HELP plz!

Find all of the first partial derivatives of f(x,y,z)=arctan y/xz


If F(x)=f(g(x)-h(x)), where g(3)=5, h(3)=4, g'(3)=3, h'(3)=1 and f'(1)=10, find F'(3). I know how to do derivatives and all, but I rlly can't figure this question out


I'm having trouble with this question on arc length: y=lnx, (squareroot)3/3 greater than or equal to x less than or equal to 1 It sounds as if you want the length of the y = ln x curve from x = sqrt(3)/3 (0.57735..) to 1. The formula for the arc length of a line y(x) is Length...

Calculus 1

Write a function that has two infinite limits at two different x-values. Write a function where both one sided limits exist at some x value but the two sided limit do not. I don't understand how this would look, please help!


What is wrong with the following reasoning??? f(x) = 2^x f'(x) = x[2^(x-1)] Although n x^(n-1) is the derivative of x^n, you cannot apply similar rules when x is the exponent and the number being raised to a power is a constant. The derivative of b^x, where b is a constant, is...

Calculus AB (AP)

Hi, I have a calculus test tomorrow and I understand how to complete all of the problems, but I am unsure behind the reasoning of taking two derivatives. Can someone please explain the following: 1. g(x)=e^(f(x)) g'(x)=e^(f(x))f'(x) 2. f(x)=Integral from 0 to 3x of the square ...

Calculus Derivatives

what's the equations of both lines through the point (2,3) that are tangent to the parabola y=x^2+x

differential calculus

use the product rule to find the derivatives of the given function y=(3x^2-8)^2


y=cos^3(12theta) find derivative using chain rule

Calculus (derivatives)

find an equation of the tangent line to the curve at the indicated point. y = -(x^1/3); (8, -2)


Find the derivatives of the function f(t)=cosh^2(4t)-sinh^2(4t). Simplify your answer completely.


. If y=cosx, find dy/d5x please show workings #thanks


Integrate ( x^2cosx)/(1+sinx)^2 dx with limits form 0 ti pi/4

Maths Calculus Derivatives

Find the first derivative for the following functions 1) f(x) = sin(cos^2x) cos(sin^3x) 2) f(x) = ( tan 2x - tan x ) / ( 1 + tan x tan 2x ) 3) f(x) = sin { tan ( sqrt x^3 + 6 ) } 4) f(x) = {sec^2(100x) - tan^2(100x)} / x


Find a formula for the derivatives of the function m(x)=1/(x+1) Please help.....Any assistance would be greatly appreciated.


How is 6#sin(#x-1)/cos^3(#x-1) the derivative of f(x)= 3sec^2(#x-1)? #= Pi (I coulnd't find the symbol...sorry.)

calculus quick question

g(x)= sqrt(1-4x^2) Can someone help me find the first and second derivatives please!


Complete the table. y = f(g(x)) u = g(x) y = f(u) y = (2x − 4)^7 u = y= This problem involves the chain rule of derivatives.


. Try this. If y=cosx find dy/d5x please show workings #thanks


Find all first and second partial derivatives of z with respect to x and y if x^2+4y^2+16z^2−64=0.

Calculus - Derivatives

Use implicit differentiation to find the second derivative y'' of the function given. x^2 + 5y^3 = 8

Calculus (Limits)

Let f be defined as follows, where a does not = 0, f(x) = {(x^2 - 2a + a^2) / (x-a), if x does not = a 5, if x = a Which of the following are true about f? I. lim f(x) exists as x approaches a II. f(a) exists III. f(x) is continuous at x = a. A. None B. I, II, and III C. I ...

maths-urgently needed

Integrate ( x^2cosx)/(1+sinx)^2 dx with limits from 0 to pi/4

Calculus (Derivatives)

Using the product rule, find the derivative of the following function: (x^1/2 cscx sinx).

Calculus: Implicit Derivatives

Compute d/dx[f(g(x))] -where f(x)=x^4-x^2 -and g(x)=x^2-7 (Note: I tried 5 times but I still got this wrong. Plz help)

Maths - Integration

Find the exact value of the intergal with limits 1 and 0 respectively for the x^2 e^2x dx.


Find the Limits. lim [t^3 + 3t^2]/[t^3 - 4t^2] t->0

Math - Calculus

how to solve limits?


A curve is defined by the parametric equations: x = t2 – t and y = t3 – 3t Find the coordinates of the point(s) on the curve for which the normal to the curve is parallel to the y-axis. You must use calculus and clearly show your working, including any derivatives you need...


find the following derivatives: f(x) = (2x+5)/(x^2-3) f'(x)= (2)*(x^2 -3)-(2x+5)*2x/(x^2-3)^2 is that correct??? f(x)= (lnx)(cos x) f'(x)= 1/x*-sinx or do i have to use the product rule?? thank you.

Calculus Review for exam grade 12, please help.

use the derivatives of y=sinx and y=cosx to develop the derivative of y=tanx


Following 2 questions are from a book at a point where L’Hopital’s Rule, Squeeze Theorem etc. have not been discussed and limits (A) and (B) as given below are to be evaluated by simple methods like algebraic simplification etc. 1. Int. of (xlogx)dx from 0 to 1. Indefinite...


Following 2 questions are from a book at a point where L’Hopital’s Rule, Squeeze Theorem etc. have not been discussed and limits (A) and (B) as given below are to be evaluated by simple methods like algebraic simplification etc. 1. Int. of (xlogx)dx from 0 to 1. Indefinite...


math question from applications of the derivatives. maths formula: V = 4/3(pi)r^3 dV = 4(pi)(3r^2) = 4(pi)r^2 But I don't understanding that how to get (3r^2) ?


Using the first of these limits, find f'(3) if f(x)=4x^2+4x-2


Evaluate the following limits (x^2 + 2x - 8)/x-2 Lim x->2


Show, using limits, that f(x) = x2 – x + 3, is continuous at x = 2.


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