Introductory Combinatorics
5th Edition
ISBN: 9780136020400
Author: Richard A. Brualdi
Publisher: Prentice Hall
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Chapter 9, Problem 14E
To determine
To prove: The inequality
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a) Sketch the y = cosh x, and indicate its properties.
b) prove that sinh 2x = 2 sinh x coshx
dx
برهن
for y=xetanh 3x + cosh¹ x² + 10
dy
Find
cosh x
Find S
dx
1-sinh 2 x
Q2. Find the points on the ellipse x²+4y² = 1, where f(x, y) = xy has its extreme value.
Q3. Find the moment of inertia about x-axis for the area bounded by the curves x = y² and
x=2y-y2 if 8 = y + 1.(20 Mark)
Q4 Find the iterated integral for the following then evaluate it: (20 Mark)
-1/√2 y2
dxdy
-1/√2 1-y2
Q8 Salve:
f√coshx-i.dx
do
Solve: So
Q₂
Qio Salve
S
Sinho + cosho
dx
4-x2
Qll Solve Sdx
√ex+1
Q12 If y = (x²+1). sech (lmx), and dy
dx
Q13 If y = /n | cschx + cothxl, Ind dy
Chapter 9 Solutions
Introductory Combinatorics
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- If y = /R/cschx + cothx|, 2nd dy 3) ans. aus. dy: x^" [ x² + x^ (1+/nx)/nx] dx + 252 cosh + + C ans. + 1 aims. aims. -2 csch'e ans. dy да = 2 12) ans. - cschx + A + Carrow_forwardHyperbolic function - Home work Q₁ show that: d (sechu) = -sechu.tanu. Ju dx Q3 show that: coth x = 1 / m² ( x + 1 | Q2 Proof that: d (sechu) = du -(054<1) u√F-4 dx In 1871 X7/1 X-1 Que Proof that: cost'x= | | x+√x=1/.. Qs show that: sinh (A+B) = SinhA. cosh B + Cosh A. sinh B Q6 Find dy, if y = x** +++ Q7 Solve; e-edxarrow_forwardQ6 cons dy= x^" [ x + x^ (1+/mx)/mx] dx Q7) aus. In (cash/ + F Qs) AMS. 252 cosh ++c +A Q₁) aus. e + A Q10) ans. + + C ams. Qu) Q₁2) ans. QIN 941. - cschx -2 csche + A dy da = 2arrow_forward
- Sketch the region of the integral dy dx. Write an equivalent double integral with the order of integration reversed. Do not solve the integral.arrow_forwardg Ske Find the area of the region bounded by the parabola x = 2y- y² + 1 and the line y = x + 1arrow_forward- | العنوان For the volume of the region in the first octant shown in the adjacent Figure. It is bounded by the coordinates planes, the plane: y = 1-x, and the surface:z = cos(лx/2), 0 ≤x≤1 Find the limits of integration for the two iterated integrals below: dz dx dy and dy dz dx Then find the volume of this region by only one of the above two iterated integrals. = cos(x/2) of y=1-xarrow_forward
- For the volume of the region in the first octant shown in the adjacent Figure. It is bounded by the coordinates planes, the plane: y = 1-x, and the surface:z = cos(лx/2), 0 ≤x≤1 Find the limits of integration for the two iterated integrals below: dz dx dy and dy dz dx Then find the volume of this region by only one of the above two iterated integrals. cos(x/2)/ y 1-xarrow_forwardNo chatgpt pls will upvotearrow_forwardFind the points of intersections of the function f(x) and its derivative. f(x)=(2x-3)√xarrow_forward
- C = (2√3)/3 or (-2√3)/3 within the interval (-2,2)arrow_forward4. [10 marks] Let T be the following tree: Find a graph G whose block graph BL(G) is isomorphic to T. Explain why your answer is correct.arrow_forward5. [10 marks] Determine whether the graph below has a perfect matching. Explain why your answer is correct. ข พarrow_forward
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