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mathematics
calculus early transcendentals 9th
Calculus Early Transcendentals 9th Edition James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin - Solutions
Sketch the region bounded by the curves.y = 3x, y = x2
Use the formula in Exercise 89 to prove the addition formula for cosine.cos(α – β) = cos α cos β + sin α sin β
Write the sum in sigma notation.1 – x + x2 – x3 + ∙ ∙ ∙ + (–1)nxn
Prove the identity. 2 tan 0 tan 20 = 1- tan0
Prove the identity.2 csc 2t = sec t csc t
Prove the identity.cot2θ + sec2θ = tan2θ + csc2θ
Prove the identity.tan2α – sin2α = tan2α sin2α
Prove the identity.sec y – cos y = tan y sin y
Prove the identity.(sin x + cos x)2 = 1 + sin 2x
If sin x = 1/3 and sec y = 5/4 , where x and y lie between 0 and π/2, evaluate the expression.sin(x – y)
If sin x = 1/3 and sec y = 5/4 , where x and y lie between 0 and π/2, evaluate the expression.cos(x – y)
If sin x = 1/3 and sec y = 5/4 , where x and y lie between 0 and π/2, evaluate the expression.cos(x + y)
If sin x = 1/3 and sec y = 5/4 , where x and y lie between 0 and π/2, evaluate the expression.sin(x + y)
Prove the identity.cos 3θ = 4 cos3θ – 3 cos θ
Prove the identity.sin 3θ + sin θ = 2 sin 2θ cos θ
Prove the identity. sin(x + y) tan x + tan y cos x cos y
Prove the identity. sin o csc o + cot ¢ 1- cos o
Prove the identity.sin2x – sin2y = sin(x + y) sin(x – y)
Prove the identity.sin x sin 2x + cos x cos 2x = cos x
Prove the identity.sin θ cot θ = cos θ
Prove the identity.sin(π – x) = sin x
Prove the identity. TT sin + x = cos x
Prove the third law of logarithms.
(a) By comparing areas, show that ln 2 < 1 < ln 3.(b) Deduce that 2 < e < 3.
By comparing areas, show that < In n
(a) Find the equation of the tangent line to the curve y = 1/t that is parallel to the secant line AD.(b) Use part (a) to show that ln 2 > 0.66.
(a) By comparing areas, show that1/3 < ln 1.5 < 5/12(b) Use the Midpoint Rule with n = 10 to estimate ln 1.5.
Evaluate E Eli + j) i=1
Evaluate E (2i + 2'). i=1
Find the limit. 3 3i lim n-00 =1 n 1 + 3i 1 + n
Evaluate 3 Σ 21-1 i=1
Prove the formula for the sum of a finite geometric series with first term a and common ratio r ± 1: a(r" – 1) r - 1 2 ar- = a + ar + ar? + ... + ar"-1 .i-1 i=1
Find the limit. 3 2i 2i lim 2 n* 1 n + 5
Find the limit. 3 lim Σ + 1 n- 00 i=1 n
Find the limit. lim 2 n0 =1 n
Prove the generalized triangle inequality: E a, < Ela|| i=1 i=1
Prove formula (e) of Theorem 3 using the following method published by Abu Bekr Mohammed ibn Alhusain Alkarchi in about ad 1010. The figure shows a square ABCD in which sides AB and AD have been divided into segments of lengths 1, 2, 3, . . . , n. Thus the side of the square has length n(n + 1)/2
Find the number n such that Ei= 78. i=1
Find the value of the sum. 2 (i3 – i - 2) i=1 “人
Find the value of the sum. E i(i + 1)(i + 2) i=1
Find the value of the sum. E(i? + 3i + 4) i=1
Find the value of the sum. E (i + 1)(i + 2) i=1
Find the value of the sum. E (3 + 2i)? i=1
Find the value of the sum. Σ2-5) i=1
Find the value of the sum. E 2i i=1 Ε
Find the value of the sum. 4 E (2' + i?) i=0
Find the value of the sum. 4 2 23-i i=-2
Find the value of the sum. 100 24 i=1
Find the value of the sum. 20 E(-1)"
Find the value of the sum. E cos kT k=0
Find the value of the sum. 6. 2 3i+1 IM
Find the value of the sum. 6 E i(i + 2) i=3
Find the value of the sum. 8 Σ (3i-2) i=4
Write the sum in sigma notation.x + x2 + x3 + ∙ ∙ ∙ + xn
Write the sum in sigma notation. 16 뚜 + 36
Evaluate each telescoping sum.a.b.c.d. E [i* - (i – 1)*] i=1
Write the sum in sigma notation.1 + 2 + 4 + 8 + 16 + 32
Write the sum in sigma notation.1 + 3 + 5 + 7 + ∙ ∙ ∙ + (2n – 1)
Write the sum in sigma notation.2 + 4 + 6 + 8 + ∙ ∙ ∙ + 2n
Write the sum in sigma notation. 23 27 inla
Write the sum in sigma notation. + + ++ 19 20
Write the sum in sigma notation.√3 + √4 + √5 + √6 + √7
Write the sum in sigma notation.1 + 2 + 3 + 4 + ∙ ∙ ∙ + 10
Write the sum in expanded form. E f(x;) Ax; Xj i=1
Write the sum in expanded form. n-1 E(-1)' j=0
Write the sum in expanded form. n+3 2 j=n
Write the sum in expanded form. Σ 10 i=1 Ε
Write the sum in expanded form. 8 Ex* k-5
Write the sum in expanded form. 2k – 1 k-o 2k + 1
Write the sum in expanded form. Σι 3 i=4
Write the sum in expanded form. i=4
Prove the second law of exponents for ex.
Prove the third law of exponents for ex.
Prove the second law of exponents.
Prove the fourth law of exponents.
Deduce the following laws of logarithms from(a) logb(xy) = logbx + logby(b) logb(xyy) = logbx – logby(c) logb(xy) = y logbx
Write the sum in expanded form. 1 Σ i + 1 i=1 i+1
Write the sum in expanded form. 5 E VE i=1
Use the addition formula for cosine and the identitiesto prove the subtraction formula (14a) for the sine function. -)- -) - sin 0 TT sin cos e cos =
Use the figure to prove the subtraction formulacos(α – β) = cos α cos β + sin α sin β y. A (cos a, sin a) B(cos B, sin B)
Graph the function by starting with the graphs in Figures 18 and 19 and applying the transformations where appropriate. y = 2 + sin xr+ 4.
Graph the function by starting with the graphs in Figures 18 and 19 and applying the transformations where appropriate.y = |sin x| -1 2 (a) f(x)= sin x 1 FIGURE 18 (b) g(x) = cos x 1+ 37 -1 y= tan x y= cot x 1 y= sin x y= cos x 1 37 -1 y= csc x y= sec x FIGURE 19
Graph the function by starting with the graphs in Figures 18 and 19 and applying the transformations where appropriate.y = 1 + sec x -1 2 (a) f(x)= sin x 1 FIGURE 18 (b) g(x) = cos x 1+ 37 -1 y= tan x y= cot x 1 y= sin x y= cos x 1 37 -1 y= csc x y= sec x FIGURE 19
Graph the function by starting with the graphs in Figures 18 and 19 and applying the transformations where appropriate. 1 y = -tan x 3
Graph the function by starting with the graphs in Figures 18 and 19 and applying the transformations where appropriate.y = tan 2x -1 2 (a) f(x)= sin x 1 FIGURE 18 (b) g(x) = cos x 1+ 37 -1 y= tan x y= cot x 1 y= sin x y= cos x 1 37 -1 y= csc x y= sec x FIGURE 19
Graph the function by starting with the graphs in Figures 18 and 19 and applying the transformations where appropriate. IT y = cos x 3
In triangle ABC, a = 4, b = 5, and c = 7. Find the area of the triangle.
Find the area of triangle ABC, correct to five decimal places, if|AB| = 10 cm |BC| = 3 cm ∠B = 107°
In triangle ABC, a = 100, c = 200, and ∠B = 160°. Find b and ∠A, correct to two decimal places.
In order to find the distance |AB| across a small inlet, a point C was located as in the figure and the following measurements were recorded:∠C = 103° |AC| = 820 m |BC| = 910 mUse the Law of Cosines to find the required distance. A C В
In triangle ABC, a = 3.0, b = 4.0, and ∠C = 53°. Use the Law of Cosines to find c, correct to two decimal places.
In triangle ABC, ∠A = 50°, ∠B = 68°, and c = 230. Use the Law of Sines to find the remaining side lengths and angles, correct to two decimal places.
Find all values of x in the interval [0, 2π] that satisfy the inequality.sin x > cos x
Find all values of x in the interval [0, 2π] that satisfy the inequality.–1 < tan x < 1
Find all values of x in the interval [0, 2π] that satisfy the inequality.2 cos x + 1 > 0
Find all values of x in the interval [0, 2π] that satisfy the inequality.sin x ≤ 1/2
Find all values of x in the interval [0, 2π] that satisfy the equation.2 + cos 2x = 3 cos x
Find all values of x in the interval [0, 2π] that satisfy the equation.sin x = tan x
Find all values of x in the interval [0, 2π] that satisfy the equation.2 cos x + sin 2x = 0
Find all values of x in the interval [0, 2π] that satisfy the equation.sin 2x = cos x
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