Calculus Homework Answers & Questions

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  • Answered x^2 + 1 =5

    X^2 + 1 =5

  • Answered Find atleast two equations of a line through ( 4,

    Find atleast two equations of a line through ( 4, 13 ) that is tangent to y = 2x^2 - 1 

  • Answered Reference angle

    What is the reference angle of 840?

  • Answered Tecniques of Differentiation

    (sinx)lnx

  • Answered Find the derivative of the function

    y= 2^x + 2/x^3

  • Answered Funciones

    Como se desarrollan las funciones inversas?

  • Waiting for answer Find the local maximum and minimum values of ##f## using bot...

    ## f(5)=1/10## is a local max. ## f(-5)=-1/10## is a local min. ##f(x)={x}/{x^2+25}## By , ##f'(x)={1 cdot(x^2+25)-x cdot 2x}/{(x^2+25)^2}={25-x^2}/{(x^2+25)^2}=0## ##= x= pm5" "...

  • Waiting for answer What is the derivative of ##1+tan^2x##?

    ##2tanxsec^2x## differentiate using the##color(blue)(" chain rule ") ## rewrite ## tan^2x = (tanx)^2## ##d/dx[ 1 + (tanx)^2] = 2(tanx) d/dx(tanx) ## ## = 2tanxsec^2x ##

  • Waiting for answer When would you use u substitution twice?

    When we are reversing a differentiation that had the composition of three functions. Here is one example. ##int sin^4(7x)cos(7x)dx## Let ##u=7x##. This makes ##du = 7dx## and our i...

  • Waiting for answer How do you find the vertical asymptotes of the function ##y=...

    The vertical asymptotes of ##y=(x^2+1)/(3x-2x^2)## are ##x=0## and ##x=3/2##. To find the vertical asymptotes we set the denominator equal to zero. ##3x-2x^2=x(3-2x)=0rArrx=0 or x=3/2## Look at the graph below. Sometimes, the denominator is equal to zero at the same x-value that makes...

  • Waiting for answer How do you find the Maclaurin series for ##cos^2 (x)##?

    ##1-x^2+x^4/3-2/45 x^6+x^8/315+\cdots## There are two methods. 1) Let ##f(x)=cos^2(x)## and use ##f(0)+f'(0)x+(f''(0))/(2!)x^2+(f'''(0))/(3!)x^3+\cdots## We have, by the and/or ,...

  • Waiting for answer How do you show that the derivative of an odd function is ev...

    I think you could do it like this: Let f(x) be the odd function we're gonna work with. So, f(-x) = -f(x), By the definition of the derivative: f'(x) = ##lim_(h- 0)(f(x+h) - f(x))/h##. We want to prove that f'(-x) = f'(x). Now, f'(-x) is: ##f'(-x) = lim_(h- 0)(f(-x+h)-f(-x))/h## . Since f(x) is...

  • Waiting for answer What is the integral of ##e^(7x)##?

    It's ##1/7e^(7x)## What you want to calculate is: ##int e^(7x)dx## We're going to use . Let ##u = 7x## Differentiate (derivative) both parts: ##du = 7dx## ##(du)/7 = dx## Now we can replace everything in the integral: ##int 1/7 e^u du## Bring the constant upfront ##1/7 int e^u du## The integral o...

  • Waiting for answer What is the integral of ##int ( 1 / (25 + x^2) ) dx ##?

    ##int(1/(25+x^2))dx=1/5 tan^-1 (x/5) +C## ##int(1/(25+x^2))dx ## ##dx/d(theta)=5tantheta## ##dx= 5sec^2theta *(d)theta## ##int(1/(25+25tan^2theta))* 5sec^2theta*(d)theta## ##int(...

  • Waiting for answer What is the x-coordinate of the point of inflection on the g...

    We find the Inflection Points of ##y## by finding the second derivative of the function (y''), and the x-values at which y'' equals 0. We look for the zeroes because at those points the concavity (or the direction in which the slope of the function ##f(x)## is trending) has leveled off; it is at...

  • Waiting for answer How do you find the integral of ##x^3 * sin( x^2 ) dx##?

    ##I=1/2(-x^2cosx^2+sinx^2)+C## ##x^2=t = 2xdx=dt, x^3dx=1/2x^2 2xdx = 1/2tdt## ##int x^3 sinx^2 dx = 1/2 int tsintdt = I## ##u=t = du=dt## ##dv=sintdt = v=int sintdt= -cost##...

  • Waiting for answer How do you find the third degree Taylor polynomial for ##f(x...

    ##ln(2)+1/2(x-2)-1/8(x-2)^2+1/24(x-2)^3##. The general form of a Taylor expansion centered at ##a## of an analytical function ##f## is ##f(x)=sum_{n=0}^oof^((n))(a)/(n!)(x-a)^n##. He...

  • Waiting for answer What is the difference between a Tangent line and a secant l...

    The to a curve at a given point is a straight line that just "touches" the curve at that point. So if the function is f(x) and if the tangent "touches" its curve at x=c, then the tangent will pass through the point (c,f(c)). The slope of this tangent line is f'(c) ( the derivative of the functio...

  • Waiting for answer The functions f and g are defined for all x€R \{ -1,0,1} by...

    General approach is to transform both sides of the equality until they start appearing similar. Consider the right hand side, we have: ##(f@g)(x) = f(g(x)) = (1/x +1)/(1-1/x) =...

  • Waiting for answer How to find average acceleration? a bird is flying south at...

    ##abs(vec a) = 5 m/s^2 ## ## theta = arctan (4/3)## by definition average acceleration over time ##t## is: ##vec a = (Delta vec v)/(t) = 1/t (vec v_2 - vec v_1)## using W-E as po...

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