KALKULUS
Nama Kelompok :Muhammad Fadlan Ariska (120402085) – KetuaRiovan Sipahutar ()Esra C. Siagian ()M. Ridho Baridwan ()Albertwan Tambunan () 5
Syiska Yana, S.T., M.T.
Exercise 117 1
a. b.
c.
Exercise 117 3
a. b. c.
Exercise 117 5
a. b. c.
Exercise 117 7
Gradient of the curve at the point (0,4) and (1,8)
At the point (0,4) → Thus the gradient At the point (1,8) → Thus the gradient
Exercise 117 9
a.
b.
Exercise 118 1
Exercise 118 3
Exercise 118 5
Exercise 118 7
Exercise 119 1
Exercise 119 3
Exercise 119 5
Exercise 119 7
Exercise 120 1
Exercise 120 3
Exercise 120 5
Exercise 120 7
Exercise 120 9
Exercise 121 1
a.b.
Exercise 121 3
a.
b.
Exercise 121 5
Exercise 121 7
Exercise 122 1
Exercise 122 3
Exercise 123 1
Exercise 123 3
Exercise 123 5
Exercise 124 1
Exercise 124 3
Exercise 124 5
Exercise 124 7
Exercise 124 9
Exercise 125 1
Exercise 125 3
Exercise 125 5
Exercise 125 7
Exercise 125 9
Exercise 125 11
Exercise 126 1
Exercise 126 3
Exercise 126 5
Exercise 127 1
Exercise 127 3
Exercise 128 1
Given x =3t −1 and y=t(t −1), determine in terms of t. Jawab: x =3t −1 y=t(t −1)= t2-t
Exercise 128 3
The parametric equations for an ellipse are x =4 cos θ, y= sin θ. Determine
a. Jawab: x =4 cos θ y= sin θ
b. Jawab:
Exercise 128 5
The parametric equations for a rectangular hyperbola are x =2t, . Evaluate when t =0.40 Jawab: x =2t
Exercise 128 7
Determine the equation of the tangent drawn to the rectangular hyperbola x =5t,
at t =2. Jawab: x =5t
y−y1 =
y − = y − =
y = y =
Exercise 129 1
A cycloid has parametric equations x =2(θ −sin θ), y=2(1−cos θ).Evaluate, at θ =0.62 rad, correct to 4 significant figures, a. Jawab: x =2(θ −sin θ) =2θ −2sin θ
y=2(1−cos θ) =2−2cos θ
θ =0.62 rad
Exercise 129 1
b. Jawab: : θ =0.62 rad = -14.43
Exercise 129 3
Exercise 129 5The radius of curvature, ρ, of part of a surface when determining the surface tension of a liquid is given by: ρ= Find the radius of curvature (correct to 4 significant figures) of the part of the surface having parametric equationsx =3t, at the point t = Jawab: x =3t
Exercise 129 5
t = ρ== ρ=
Exercise 129 5
(b) x =4 cos3 t, y=4 sin3 t at t = rad Jawab: x =4 cos3 t
t = rad ρ== ρ=
Exercise 130 1
a) misal
(c) misal
(b) misal
Exercise 130 3Differentiate the following with respect to y: Jawab: (a) misal
(b) misal
(c) misal
Exercise 131 1
Determine Jawab: misal , = =
= =
Exercise 131 3
Determine Jawab: misal , = =
= =
Exercise 131 5
Determine given z = 2x3 ln y Jawab: misal , = =
=
Exercise 132 1
Jawab: =
Exercise 132 3
Given evaluate when and y=2 Jawab: = and y=2
Exercise 132 5
Jawab: =
Exercise 132 7
Jawab:
=
Exercise 132 9Determine the gradients of the tangents drawn to the circle at the point where x =2. Give the answer correct to 4 significant figures Jawab: = and y
Exercise 132 11
Determine the gradient of the curve at the point (1,−2) Jawab: misal
Exercise 133 1
Exercise 133 3
Exercise 133 5
Exercise 133 7
𝑥=1
Exercise 134 1
Exercise 134 3
Exercise 134 5
𝑥=1
Exercise 135 1
a.
b.
c.
Exercise 135 3a.
b.
Exercise 135 5
a.
b.
Exercise 136 1
a. b.
Exercise 136 3
a. b.
Exercise 136 5
𝑑𝑑𝜃
𝑦=𝑑𝑑𝜃
52𝑐𝑜𝑠𝑒𝑐− 1
𝜃2
𝑑𝑦𝑑𝜃
=52∙
−2
𝜃 √𝜃2−22𝑑𝑦𝑑𝜃
=−5
𝜃√𝜃2−22
a.
b.
Exercise 136 7
Exercise 136 9
a.
b.
Exercise 136 11
a. b.
Exercise 137 1a. b.
c.
Exercise 137 3
a. b. c.
Exercise 138 1
a. b.
Exercise 138 3
a. b.
Exercise 138 5
a. b.
Exercise 138 7
a. b.
Exercise 138 9
a. b.
Exercise 138 11
a. b.
Exercise 138 13
a. b.
Exercise 138 15
a. b.
Assingment 8 1
a.
b.
c.
Assingment 8 1
d.
Assingment 8 3
Assingment 8 5
Assingment 8 7
Assingment 8 9
Assingment 8 11
In terms of yIn terms of x
Assingment 8 13
Assingment 8 15