Kalkulus

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