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  1. J

    Differentiate: r=r cos(theta)i+r sin(theta)j

    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...
  2. J

    Find the inverse of the polynomial.

    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...
  3. J

    Implicit exponential differentiation?

    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...
  4. J

    Log function e^(ln12/2)?

    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...
  5. J

    Derivative of inverse trig functions.

    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...
  6. J

    Where am I going wrong on implicit differentation?

    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) =...
  7. J

    Why is the answer half of my answer?

    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...
  8. J

    I don't understand the meaning of f^(39)(pi/2)?

    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...
  9. J

    Epsilon Delta limits

    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...
  10. J

    Limit at infinity, no vert asymptote, why?

    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...
  11. J

    Tan[1/2 arcsin(-7/25)]

    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...
  12. J

    Tan[arctan(2/3) + arccos(8/17)]

    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...
  13. J

    Cos theta=pi/2 hint pi/2 is not an angle.

    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...
  14. J

    Trig should I start by squaring both side?

    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...
  15. J

    Trig solution, tanx+secx=1

    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
  16. J

    How to solve trig equations?

    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...
  17. J

    Trig proof, I am getting a neg instead of pos.

    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...
  18. J

    Having trouble setting up this Trig problem.

    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...
  19. J

    Reversing angular and linear formulas to find rpm.

    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...
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