can you please complete #4. thanks 1. Determine r (t)and v(t) given a(t) e i+2tj

Question

can you please complete #4. thanks

1. Determine r (t)and v(t) given a(t) e i+2tj+(t+)k with initial velocity, v(0) i+k and initial positionr(0)- 2i j+k 2. A projectile is fired from ground level at an angle of 30° upward from horizontal. Determine the range of the projectile if the initial velocity is 75 feet per second. 3. sketch the domain of the function f (x,y) V4- x2 4yz 2x 4. show that the function f(x,y) y has no limit as (x, y) approaches (0,0) 5. verify the conclusion of clairaut's Theorem holds for u x -3x y 6. Evaluate all first order partial derivatives for f(x.) e dt. (Hint: Review the Fundamental Theorem of Calculus in section 5.3) 7. Find the equation of the tangent plane to the surface x +2xy- yz +:2 7 at the a point (1, -1, 3). National Weather Service (http://www.noaa.gov/), is The from the

Explanation / Answer

f(x,y) = 2x2y / (x2+y2) let x, y both ->0 along the straight line y=mx 2

LIm x->0, y->0 ( 2x2 (mx2)) / ( x4+ m4x4)

= Limx->0, y->0 ( 2m x4) / x4(1+m4)

= Lim x,y ->0 2m / (1+m4) the value depends on the slope of the line

for a different line the value 'm' differs and hence the limit differs

as the value of the limit is not unique

hence the limit doesnt exist

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