Calculus Homework Answers & Questions
Help With Calculus Homework
At the centre of any mathematics field and nearby sciences lies calculus. Generally speaking, calculus is aimed at applying mathematics to observe and analyze change. The origins of calculus date back to the 17th century, when Isaac Newton, along with other outstanding scholars, developed a new field to deal with complex problems that could not be solved using basic algebra mechanisms and concepts.
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Answered Integration by parts.
The tuitorial entails solving integrals using integration by parts.This metod of integration requires the first step to identify u dv from the integral and this is achieved by applying the rule rule of the thumb using the acronym;LIATE whose letters represent five functions to be encountered in th...
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Waiting for answer 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
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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}={25x^2}/{(x^2+25)^2}=0## ##= x= pm5" "...
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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 ##
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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...
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Waiting for answer How do you find the vertical asymptotes of the function ##y=...
The vertical asymptotes of ##y=(x^2+1)/(3x2x^2)## are ##x=0## and ##x=3/2##. To find the vertical asymptotes we set the denominator equal to zero. ##3x2x^2=x(32x)=0rArrx=0 or x=3/2## Look at the graph below. Sometimes, the denominator is equal to zero at the same xvalue that makes...
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Waiting for answer How do you find the Maclaurin series for ##cos^2 (x)##?
##1x^2+x^4/32/45 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 ,...
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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...
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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...
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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(...
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Waiting for answer What is the xcoordinate 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 xvalues 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...
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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##...
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Waiting for answer How do you find the third degree Taylor polynomial for ##f(x...
##ln(2)+1/2(x2)1/8(x2)^2+1/24(x2)^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!)(xa)^n##. He...
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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...
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