Given an ellipse x2/a2 +y2/b2= 1, a  b, find the  equation of the set of all points from which there are two tangents to the ellipse whose slopes are reciprocals

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 7E
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Given an ellipse x2/a2 +y2/b2= 1, a  b, find the  equation of the set of all points from which there are two tangents to the ellipse whose slopes are reciprocals

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6.8. The Integral
233
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6.8.5. Evaluate each of the following:
hE Edit PDF
(a) lim n-3/2 E VE.
k = I
Create PDF
(b) lim E
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6,8.6. Find the integral part of E n-2/3. (Hint: Compare the area under
f(x) = x
[2, 10° + 11.)
-- 2/3
over [1, 10° + 1] with the area under g(x) = (x – 1)-2/3
over
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6.8.7. Suppose that f and g are continuous functions on [0, a], and suppose
that f(x) = f(a – x) and g(x) + g(a – x) = k for all x in [0, a], where k is a
fixed number. Prove that
Seloct Ce
f(x)g(x) dx = }k f(x)dx.
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forms & agreements
Use this fact to evaluate
x sin x
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dx.
Jo 1+ cos?x
Transcribed Image Text:[Loren_C._Larson]_Problem-solving_through_problems.pdf - Adobe Acrobat Reader DC File Edit View Sign Window Help Home Tools [Loren_C._Larson]_... x Sign In 245 | 345 125% Search 'Strikethrough' 6.8. The Integral 233 Export PDF 6.8.5. Evaluate each of the following: hE Edit PDF (a) lim n-3/2 E VE. k = I Create PDF (b) lim E Adobe PDF Pack Convert files to PDF and easily combine them with other file types with a paid subscription 6,8.6. Find the integral part of E n-2/3. (Hint: Compare the area under f(x) = x [2, 10° + 11.) -- 2/3 over [1, 10° + 1] with the area under g(x) = (x – 1)-2/3 over Select File to Convert to PDF 6.8.7. Suppose that f and g are continuous functions on [0, a], and suppose that f(x) = f(a – x) and g(x) + g(a – x) = k for all x in [0, a], where k is a fixed number. Prove that Seloct Ce f(x)g(x) dx = }k f(x)dx. Create, edit and sign PDF forms & agreements Use this fact to evaluate x sin x Free 7-Day Trial dx. Jo 1+ cos?x
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