math

Math263Exam2Revi.ee# Section 13.213.3

, 14.1-1406

④ Exam problems may look like problems on this Review sheet, homework , quizzes, or class problems.. ↳ study everything !!

1) Find the unit tangent vector Flt) at the point w/given value of the parameter t a) Fct)=L 4te

't

, 2 tan

'(t) , get> , t =o

b) Flt) -- 4VII +2Ej + 4th , t--I

2)Evaluate the following integral 14¥I+7¥

3) Find parametric eqns for the tangent line to thecurve w/ the given parametric equations at the specified point.

*e- "t cos htt)

, y - - e-45in(4T)

, z=E4t ; (1,0, I)

4) Find Fct) if F'ft)=3t'T t 4t3jtVI Te and FCD= I t j

5) Find the length of the curve Fft)= cos19T) itsin (at)j -19 In ( cosGDI t f-OR oETETH

G) Consider the vector function TH)= 29VIE, eat, e-

at > a) Find Fct) b) Find Nlt) c) Find curvature KH)

O7) Find F. IT, B- at (6,0, O) , FH)=L6cosIt), 6sink), 6In(cosHD)

8) Reparametrize the curve with Respect to the arc length with tZo Fct) = 4to t (5-at)j t (7-13T)K

9) Find eggs of the normal plane & osculatingplane at ( o,T, -5) x= 5sin (3t) , y

= t , 2-=5cos(3T)

10) Find & Sketch the domain of the function f(x.g)=In (4- XZ-4yd

a)Sketch the graph of the function fcxy) = II- 4×-5y

(2) Match contour curves with surfaces

(3) Draw a contour map of the function fcx.gs = XZ- ya

14) find the limit , if it exists

a)¥:*..CI:97) Dc!iiIwnI÷, 15) find hcx,g)=gCflx.D) & the set which his continuous

gct) = telnet) & f-(x.g) =3-xy2tX2y2

b) Find the first partials a) flag)=xsincxg) b) w =

Ut ✓ 8

(7) Find equation of the tangent plane @ (1,3, -10) for 2=2×2 t y ' -Ty

I(8)Find the differential dz, z=×3y8 19) find d¥ where z=×y9-Ey , X=tZtl , y=tZ

-I

↳Find IT and IF for 2-= tan Cua) , u= as-15T , V=5S -2E

a) Find d# ; 9g coscx) =x2tyZ

⇒ Find the directional derivative off at (3,1) & direction O= -% -f(x.g)=✓2x -13g

237 Find the directional derivative at (o,Hs) w/ direction vector J=L-6,85 f-Cx.g)=3 in ly)

24) Find the maximum Rate of change of f at (16,3) and the direction in which it occurs fcx,g) = SryVI

257 Find the gradient of f-(x.g) =sin(2x-13g)

267Find the equation of the tangentplane of y=X2 -ZZ @ (10,19,9)