Homework Statement
This is a problem from Dynamics but I'm mostly having trouble with the calculus.
Derive an expression for the position, velocity, and acceleration of a machine in terms of: r, \dot {r}, θ, \dot{θ}, \ddot{r}, \ddot{θ}, .
r = length of the arm
θ = angle of the arm to the...
Homework Statement
Find (f^{-1})'(a) of: f(x)=\sqrt{x^{3}+x^{2}+x+22} ; a=5.
Homework Equations
(f^{-1})'(a)=\frac{1}{f'((f^{-1})(a))}
The Attempt at a Solution
Well, I know to find an inverse: I need to set the equation equal to y, solve for x, then swap x and y. But I don't...
Homework Statement
Find an equation of the tangent line to the curve xe^y+ye^x=1 at point (0,1).
Homework Equations
I do not recall seeing the Implicit Function Theroem before, I even went back in my book (Stewart Calculus 6th) to check. I found this post but it does not help me...
Homework Statement
The full problem is y=e^(x/2) and y=e^(-x) revolved around the x-axis, from [ln6,ln12].
The part I'm struggling with is evaluating 2e^(ln12/2) and 2e^(ln6/2).
I am just reviewing for my Calculus 1 final.
Homework Equations
The Attempt at a Solution...
Homework Statement
Find the derivative:
y=sec-1(1/2t3)
Homework Equations
\frac{\frac{du}{dx}}{|u|\sqrt{u^2-1}}
The Attempt at a Solution
I have an example to follow, but I dont know how step 1. became step 2.?...or more exactly the last part under the radical? (1-4t^6) instead...
Homework Statement
Determine the equation of a tangent line to a curve at the given point.
3x2+xy+2y2=36 , P(2,3)
Homework Equations
The Attempt at a Solution
3x2+xy+2y2 = 36
finding the derivatives of each term I get:
6x+xy'+y+4yy' = 0
xy'+4yy' = -6x-y
y'(x+4y) =...
Homework Statement
The driver of a car traveling at 71 ft/sec suddenly applies the brakes. The position of the car is s = 71t - 20t2, t seconds after the driver applies the brakes. After how many seconds does the car come to a stop? Round your answer to the nearest tenth.
Homework...
I don't understand the meaning of f^(39)(pi/2)??
Homework Statement
Find the indicated derivative of f(x)=sin x and evaluate it at x=pi/2.
f^{(39)}(\pi/2)=
Homework Equations
The Attempt at a Solution
I'm not sure what the f^39 means??? And it could be f(39)(pi/2)??? but...
Homework Statement
Suppose |f(x)-5|<0.1 when 0<x<5.
Find all values \delta>0 such that |f(x)-5|<0.1 whenever 0<|x-2|<\delta
Homework Equations
The Attempt at a Solution
I know that 0<|x-2|<\delta
2-\delta<x<2+\delta
\delta=2
but how does this part of the equation help me find...
Homework Statement
Find the vertical asymptote(n) and evaluate the limit as x \rightarrow n^-, x\rightarrow n^+, or state Does Not Exist.
Homework Equations
\frac{\sqrt{4x^2+2x+10}-4}{x-1}
The Attempt at a Solution
I have taken the limits at \pm\infty=2,-2 and understand those are my...
Homework Statement
\tan[\frac{1}{2} \arcsin(\frac{-7}{25})]
The Attempt at a Solution
I'm not sure how to take 1/2 the arcsin, should this use the half-angle formula?
Normally I would draw a triangle using the sin value (-7/25), then find the tan value (24/25), but the 1/2 is...
Homework Statement
tan[arctan(2/3)+arccos(8/17)]
Homework Equations
tan(u+v)=\frac{\tan u+\tan v}{1-\tan u\tan v}
The Attempt at a Solution
After drawing 2 triangles for arctan and arccos (both in Quadrant 1), and inserting them into the addition formula for tan, I get...
cos theta=pi/2....hint pi/2 is not an angle.
Homework Statement
\cos\theta=\frac{\pi}{2} HINT:The real number \frac{\pi}{2} is not an angle.
Homework Equations
The Attempt at a Solution
I tried 0=\cos^{-1} \frac{\pi}{2}, but that equals no solution.
And if \frac{\pi}{2} were...
Trig...should I start by squaring both side???
Homework Statement
Fing the solutions that are in the interval [0,2\pi)
\tan 4t-\tan 7t=1+\tan 7t\tan 4t
Homework Equations
Use an addition or subtraction formula.
\tan(a+b)=\frac{\tan a+\tan b}{1-\tan a\tan b}
The Attempt at a...
Homework Statement
tanx+secx=1
Homework Equations
The Attempt at a Solution
tanx+secx=1
tanx=1-secx then square both sides???
\tan^2 x= 1-2\sec x+\sec^2 x\sec^2 x-1=1-2\sec x+\sec^2 x2-2\sec x=0\sec x=0 No Solution
Homework Statement
8cos2\theta-4\sqrt{3}=0
Homework Equations
I don't have one.
The Attempt at a Solution
I am really not sure where to begin, our lesson tonight was lacking detail.
I guess start by addding 4\sqrt{3} to the right side
Then what? I don't think I should...
Homework Statement
[cscx/(1+cscx)] - [cscx/(1-cscx)] = 2 sec^2 x
Homework Equations
prove the left side equals the right side
The Attempt at a Solution
1. get common denominator and subtract, [cscx(1-cscx)-cscx(1+cscx)]/[(1+cscx)(1-cscx)]
2. distribute cscx in numerator...
Homework Statement
Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution θ (see the...
Homework Statement
A simple model of the core of a tornado is a right circular cylinder that rotates about its axis. If a tornado has a core diameter of 200 feet and maximum wind speed of 240 mi/hr (or 352 ft/sec) at the perimeter of the core, approximate the number of revolutions the core...