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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
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2)find all (^) points on the (^) curvey:osx, (^) ox22x, where thetan^ lineis^ parallel to^ line - -X
C
y = - x (^) y= cosX him4X 5x + 0(4x 16x3x^ + 2) y^
y = -Sint
1 = Sinx,Sink):X=
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)(
zy E^ = 2 π(Sin(-4x)^ (cost
= 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 = Y X (^) interceptP(-2,0) and (^) 12,0)
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