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Use L''hopital''s rule since lim X-->0 1-cos(x)/1-cos(4x) is in the indeterminate form 0/0 when we apply the limtso by l''hoptital''s rule differentiate the numerator and denominatiorso we get lim x-->0 sin(x)/4sin(4x) again in the indeterminate form when we apply limit so again use l''hopitals'' rulelim x-->0 cos(x)/16cos(4x) now if u apply the limit we get it as 1/16so lim x--->0 1-cos(x)/1-cos(4x) = 1/16
Q. How to Subtract fractions with the same denominators? Ans. Subtracting fractions is basically the same as adding them. If you don't know how to add fractions, you shoul
Tangents with Parametric Equations In this part we want to find out the tangent lines to the parametric equations given by X= f (t) Y = g (t) To do this let's first r
The manager of a specialty store marks up imported products 110%. If a vase imported from Italy costs him $35, what price tag will he put on the item? To ?nd out the price he s
Let E; F be 2 points in the plane, EF has length 1, and let N be a continuous curve from E to F. A chord of N is a straight line joining 2 points on N. Prove if 0 and N has no cho
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A printer which sells for $190 is on sale for 20% off. What is the sale price of the printer? The printer is 20% off. That means that it is 80% of its original price (100% - 2
Solve 4 cos(t )= 3 on[-8,10]. Solution : Here the first step is identical to the problems in the previous section. First we need to isolate the cosine on one side by itself & t
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Definition 1: Given the function f (x ) then 1. f ( x ) is concave up in an interval I if all tangents to the curve on I are below the graph of f ( x ) . 2. f ( x ) is conca
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