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Extrema : Note as well that while we say an "open interval around x = c " we mean that we can discover some interval ( a, b ) , not involving the endpoints, such that a < c < b . Or, in other terms, c will be contained somewhere within the interval and will not be either of the endpoints.
Also, we will collectively call the minimum and maximum points of a function the extrema of the function. Thus, relative extrema will refer to the relative minimums & maximums whereas absolute extrema refer to the absolute minimums & maximums.
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Properties 1. ∫ b a f ( x ) dx = -∫ b a f ( x ) dx . We can interchange the limits on any definite integral, all that we have to do is tack a minus sign onto the integral
Q. Show Inverse Trigonometric Functions? Ans. Many functions, including trig functions, are invertible. The inverse of trig functions are called ‘inverse trig functions'.
Rates of Change and Tangent Lines : In this section we will study two fairly important problems in the study of calculus. There are two cause for looking at these problems now.
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How do you find the area of a circle given the diameter?
the limit of f(x) as x approaches 5 is equal to 7. write the definition of limit as it applies to f at this point
Tests for relative minimum For a relative minimum point there are two tests: i.The first derivative, which is (dy)/(dx) = f´(x) = 0 ii.The second derivative, which i
Find the length of the second diagonal of a rhombus, whose side is 5cm and one of the diagonals is 6cm.
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