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Math Project 2: Finding Points on a Curve and Tangents, Quizzes of Calculus

A math project that involves finding points on a curve and tangents. The project includes finding the limit of a function, solving equations, and calculating slopes of tangents. step-by-step instructions and equations to solve the problems. The project is suitable for advanced math students who are studying calculus and trigonometry.

Typology: Quizzes

2022/2023

Available from 03/11/2023

gabriel-gamez-ortega
gabriel-gamez-ortega 🇺🇸

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bg1
Math
Project
2)
find
all
points
on
the
curvey:
osx,
ox22x,
where
the
tan
line
is
parallel
to
line
-
-
X
1)
find
the
Limit
him
(4x-16x25x+0)
X
->
X
->
C
"
y
=
-
x
y
=
cosX
him
4X1642
5x
+
0(4x
16x
3x
+
2)
y
=
-
1
y
=
-Sint
-
looking
for
x
7
(4x
64
-
5x
+
8
1
=
Sinx,
Sink):
X=
-
(5x
+
0)
=
3x
-
8
=
Sinx
I
him
*-(1
-
sx
+
1)
y=
cos()
y
=
0
P(E,0)
mtan=-1
X
-
84x64
-
5x
+
5
Point
slope
I
=S
Gina
"
-0
=
-x-g
=
y
=
-
x
+
=P(Y2,0)-
8
I
-
b
----------
x
S
3)
Find
the
value
of
(fg)
at
the
given
value
of
X
-
At
the
two
points
where
the
tzig
ty_
i
f(w)
=
Sin
is
u
,
=
-
x4
=
8
4
=
-
8
What
is
the
common
slope
of
these
tangents
(f.g)
=
(in+(x)(
+
(
-
x)
x2
+
2xy
+
y2
=
4
S
=
(Sin
+4x)
-
4
2x
+
2y)
+
2x))y
+
xyy
=
xy))(og)
=
2(sin(
-
xx))(cs(
xx)(-1)
-
1
2x
+2y
+2xy
+
2y3
=
0
2xy'
+
zyy
=
-
2x
-
zy
E
=
2
π(Sin(
-4x)
(cost
-
ix)
-
1
Substituting
in
8
y
=
2x
-
2y
(
=
-
24
(sn
-
)
(asto
-1
2x
+
2y
=
-
24
(0)(1)
-
1
making
y
=
0
x2
+
2xy
+
y
=
=
y
I
=
-
1
x2
+
xxy
+
5
=
4
W
x
2
=
4
x
=
Y
X
intercept
P(-2,0)
and
12,0)
--------
x
=
=
2
Sinde"
for
$2
+
2
xy
+
y2
=
4
I
reta
mtan=-1
2x
+
2y
+
exy'
+
2yy1
=
0
2xy
+
2yy1
=
-
2x
-
zy
X
=
t0
=
E
=
-
1
y(2x
+
zy)
=
-
2x
-
zy
-
20
y
=
=
=
=
e

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Math Project

2)find all (^) points on the (^) curvey:osx, (^) ox22x, where thetan^ lineis^ parallel to^ line - -X

  1. find^ the^ Limit^ him^ (4x-16x25x+0)

X ->

X ->

C

y = - x (^) y= cosX him4X 5x + 0(4x 16x3x^ + 2) y^

y = -Sint

  • looking^ for^ x 7 (4x^

64 - 5x + 8

1 = Sinx,Sink):X=

  • (5x + 0) = 3x- 8 = (^) Sinx I

him *-(1-^ sx^ +^ 1)

y=cos()^ y=^0

P(E,0) mtan=- X-84x64-^ 5x^ +^5 Point (^) slope I =S Gina

-x-g = y=^ -^ x^ + =P(Y2,0)- (^8) I (^) - b


x S^ 3)Find the^ value of^ (fg) atthe^ given value^ of^ X

Atthe two (^) points wherethe (^) tzig ty_ i f(w) = Sin isu , =- x4= 8 4 =^ - 8 Whatis thecommon slope of these tangents (f.g)

(in+(x)(

  • (^) (- x) x2 + 2xy + y2= 4 S (^) = (Sin +4x)
  • 4 2x + 2y) + 2x))y + xyy = xy))(og) = 2(sin(- xx))(cs(xx)(-1) - 1 2x +2y +2xy + 2y3 =^0 2xy' + zyy =^ -^ 2x^

zy E^ = 2 π(Sin(-4x)^ (cost

  • ix) - 1 Substituting in^8

y

= 2x - 2y

(^24) (sn- ) (asto - 2x + 2y = -^24 (0)(1) - 1 making (^) y =^0 x2 + 2xy + y=^ = y I (^) = - 1 x2 + xxy + 5 = 4 W

x 2 =^4

x = Y X (^) interceptP(-2,0) and (^) 12,0)

x == 2 --------

Sinde" for^ $^2 +^2 xy + y2 =^4 I reta^ mtan=- 2x + 2y + exy' + (^) 2yy1 = 0 2xy + 2yy1 =^ -^ 2x^ - zy X^ =^ t0^ = E = - 1 y(2x + zy) =-2x^ - zy -^20 y

=== e