Show all work. 1. Find two nonnegative real numbers x and y such that x +...
please answer both of them and show all the steps , (b) Find or show the limit does not exist:linm (x, y) → (0,0) x2 + y2 8, (b) Show that the following limit does not exist 2 lim (x, y) → (0,0) x2 + y2 , (b) Find or show the limit does not exist:linm (x, y) → (0,0) x2 + y2 8, (b) Show that the following limit does not exist 2 lim (x, y) → (0,0) x2...
1. Find lim(x,y)=(1,1) x2-y2 2xy 2. Show that lim(x,y)-(0,0) 21 z does not exist 3. Show that lim(x,y)=(0,0) z?”, does not exist 4. Find lim(x,y)=(0,0) eye if it exists, or show that the limit does not exist
find the limits analytically, show all steps x²–8 1. lim *+2 X-2 2. lim x3 Vx+1-2 x-3 1 3. lim 3+ x 3 x2 - 2x -15 4. lim *+-3 x2 + 4x +3 x0 X (4+ x)-16 5. lim X>0 x² - 4 6. lim 1+2 r -8 x x+sin x 7. lim 10 X sin²x 8. lim :-) x 3 sin(4x) 9. lim *** sin(3x) r? 10. lim 1981-COSI 1 11. lim x → X-1 = 1 12....
3. Find nonnegative numbers x and y, x+y=90, such that xy is maximized. 4. (Revenue) A local club is arranging a charter flight to Hawaii. The cost of the trip is $1600 each for 90 passengers, with a refund of $10 per passenger for each passenger in excess of 90. (a) Find the number of passengers that will maximize the revenue received from the flight. (b) Find the maximum revenue.
2. Find the limits of the following functions if they exist. Show all necessary work. If the limit is co or -00, then state this rather than that it does not exist: (2 points each) a. lim x+3 V6x-2-4 x-3 b. lim arctan(3x) x sin(x) 3. Find the average value of the function f(x) = 4x2 + 8x -1 on (-1, 3).
1. Consider XPy4 lim (x,y)=(0,0) x2 + y2 Compute the limit along the two lines y = 0 and y = mx. 2. Let F(x, y) = sin(x2y?), where x = sin(u) + cos(v) and y = eutu. Use the chain rule (substitution will earn zero credit) to find ƏF au
1. Express the limit as a derivative and evaluate. 17 lim 16+h-2 lim 2. Calculate y. tan x 1 + cos x y sin(cos x) y= sec(1 +x2) x cos y + sin 2y xy Use an Implicit Differentiation] 3. Find y" if x, y,6-1. [Use Implicit Differentiation] 4. Find an equation of the tangent to the curve at the given point. 121 12+ 1 [Use Implicit Differentiation] 4. Find the points on the ellipse x2 + tangent line has...
Find the limit. lim (5 sin ?x+ 5 cos?y + sec?z) P(7.7,0) lim (5 sin?x+5 cos?y + sec z) = (Simplify your answer.) P-(7.7.0)
Find the limit, if it exists, or show that the limit does not exist. 1. lim (x²y3 – 4y?) (2,y)+(3,2) 2. lim 24 - 4y2 (x,y)+(0,0) x2 + 2y2 3. Find the first partial derivatives of the function of f(x,y) = x4 + 5.cy 4. Find all the second partial derivatives of f(x,y) = x+y + 2.x2y3 5. Find the indicated partial derivatives. f(1, y) = x^y2 – røy ; farzz, fryz
Show that if x and y are real numbers, x2 + y2 >= 2xy and (x + y)2 >= 4xy; When does equality hold (with proof)? Show that if x and y are real numbers, x2 + y2 2xy and (x y) 2Hry. When does equality hold (with proof)?