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Doug C.'s Resources

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Another way to do this problem without calculus. Find the equation of the line that passes through (-3,3) and is perpendicular to the given line (the slope of the perpendicular must be 3/5. Once you have the two equations find the point of intersection (perhaps by the substitution method). https://www...

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A good strategy for solving this problem might be to make up a specific example and think about how you would go about it then (for example let a=36). That said, we can write the equation of the tangent line passing through (x0, y0) by finding y' (implicitly), getting the slope, and then using point-slope...

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A good strategy for solving this problem might be to make up a specific example and think about how you would go about it then (for example let a=36).   That said, we can write the equation of the tangent line passing through (x0, y0) by finding y' (implicitly), getting the slope,...

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When x= 0, y = +/- 1/2. So find the equation of the tangent line at (0,1/2) and (0, -1/2).   Finding an explicit formula for y' using implicit differentiation is a formidable task. Instead just use implicit differentiation, leaving the result as you find it. Then substitute 0 for...

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Hi Abigail.   How about I give you some hints to get you started. You will need formulas for the volume of a right circular cylinder and a sphere. You will also need a formula for the surface area of those objects. The problem does not state whether the "floor" of the observatory...

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Hi Daniel, My guess is that you perhaps have not learned how to find the derivative of a function. The intent of the problem likely is to evaluate the limit directly. If that is the case:   The idea is to find something we can multiply numerator and denominator by so that the "h"...

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Hi April,    The given info is the same as telling you the function (line) passes through the points (0,7) and (3,1). Calculate the slope between those two points, then use either point-slope or slope-intercept to write the equation of the line.    Once you have...

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Since the directions indicate you must use theta between -pi/2 and pi/2 when (x,y) is in the 2nd or 3rd quadrant you will have to use the negative square root of X2 + y2.   For part a) r = sqrt(4+9) = sqrt(13).   Theta = tan-1(y/x) = tan-1(-3/2) = -0.983 radians...

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You should have a theorem in your text book indicating that for x n the radius of convergence you can find MacLaurin for f(t) in this case t2et^2, then integrate that series term by to get a power series representation for the integral in question. The assumption here is that you know how to find...

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f(0)=1, so a+bcos0 = 1, or A) a+b = 1.   f(pi/4) = 3/2, so B) a+bcos(cpi/4) = 3/2   Let g(x) equal the derivative of f. g(x) = -bcsincx.   g(pi/4) = 3/2, so C) -bcsin(cpi/4) = 3/2.   Getting ugly. At this point there are 3 equations...

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Hi Imani,   Do you know the three identities for the cosine of twice an angle? If not, take time to locate them in your trig book.   One of them is cos2x = 1-2sin2x. Since you are given sinx = 9/41, substitute that value into the aforementioned identity and simplify.

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related rates (answer)

Hi Julia,   Are you using formula for area of equilateral triangle is A = s2√3/4? If so, then dA/dt = 2s√3/4 ds/dt= s√3/2 ds/dt.    Now try substituting given values into that equation.

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Likely the expectation is for you to use the identity for the tangent of the sum of two angles.   tan(x+y) = (tan x + tan y)/(1-tanxtany).   In this case x = arc sin(3/7) and y = arc cos 4/5.    To find the tangent of x and tangent of y there are...

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Making a table of values can be a pain. Calculator optional, but highly desirable. Check out the following graph to get the idea. https://www.desmos.com/calculator/otd8ormj0f   Enable and disable the functions for f, g, h to get an idea of what the point is.

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Hi Notroe,   Whenever I see a problem like this (asked to solve for x and four terms on the left side and 0 on the right) I get suspicious that factoring by grouping might lead to something.   Try: 2sinx(2cosx - √3) - √2(2cosx - √3) = 0   (notice...

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Hi Don,   If this is written as f(x) = 2e-5x^2, then you can ask the question does f(x) = f(-x). If so this is an even function and is symmetric about the y-axis.    Find f'(x) to determine increasing/decreasing. f'(x) = -20xe-5x^2. This will only equal 0 when x =...

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