Tan x antiderivative
[DOC File]AP Calculus Free-Response Questions
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147. Let f be the function defined by f(x) = (1 + tan x)1.5 for < x < a. Write an equation for the line tangent to the graph of f at the point where x = 0. b. Using the equation found in part a, approximate f(0.02). c. Let f -1 denote the inverse function of f. Write an expression that gives f -1(x) for all x in the. domain of f -1. 148.
[DOC File]What is an Antiderivative
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Give the definition of an antiderivative. Antidifferentiation . is obviously the reverse process of differentiation. Given a function f, we say that F is an . antiderivative. of f provided that F’ = f. In order to find antiderivatives, slope fields are used. Begin with the simplest case, a function whose graph has a constant slope. f(x) = y0 ...
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(Note: tan -1 x = arctan x ) Find the position of the particle at time t=2 . (Calculator Allowed) 12. If f is the antiderivative of x 2 1+ x 5 such that f 1 =0 , then what does f 4 = ? (Calculator Allowed) 13. Insects destroyed a crop at the rate of 100 e -0.1t 2- e -3t tons per day, ...
[DOCX File]§Appendix C Sigma Notation - College of Arts and Sciences
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rectangle, width Δ x of subinterval, height f( x i * ) , x i * sample point for i TH rectangle. Take the limit as the number of rectangles increases to ∞ . Example. Estimate the area A under the graph of f x =x from x=0 to x=1 .
[DOC File]Calculus II - Valencia College
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What is (1) where Z(x) = tan[Y(x)], Y (1) = and (1) = –5? Ans: -20. 43. The town of Jalapeño is 20 kilometers north-northeast of the town of Anacho, and the town of Habanero is 30 kilometers southwest of Anacho. How far is it from Habanero to Jalapeño? ... Find the antiderivative of x sinh x that has the value 10 at x = 0. Ans:
[DOC File]Calculus II - SJSU
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Integration by substitution is the method use try after you decide you can't find the antiderivative by inspection. An Integration by Parts Problem: Integration by …
[DOC File]Derivatives
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xn ex ex sin x - cos x cos x sin x tan x - ln | cos x | tan x ln x ln x x ln x – x , x > 0 ax Implicit Differentiation. To implicitly differentiate an expression of the form, (say), , we take . Where and we use the product rule for to get: We then “solve for” : (Then one can calculate the value of the derivative at a given point by ...
[DOCX File]Louisiana State University
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Let . F be any antiderivative of f on an interval I . Then all the antiderivatives of f on I have the form F+C , where C . is an arbitrary constant. ... d dx tan -1 x a = a a 2 + x 2 dx a 2 + x 2 = 1 a tan -1 x a +C . d dx ( sec -1 x a )= a x x 2 - a 2 dx x x 2 ...
[DOCX File]§4.1 Maximum and Minimum Values - College of Arts and ...
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f ' x = 1 ( x 2 -9)-x(2x) x 2 -9 2 = - x 2 -9 x 2 -9 2
[DOC File]Calculus I
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An experiment involves finding the area to the right of the y-axis and under the curve y = tan x as x increases. Find the instantaneous rate of change in the area when x = π/3. ... In #5 and #6, find the antiderivative. 5.) 6.) In #7 and #8, evaluate the definite integral. Give EXACT answers only and simplify your answers completely. 7.) 8.)
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