Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y,z) = (x / y) – yz, Po(1,1,3) The direction in which the given function f(x,y,z) = (x/y) - yz increases most rapidly at Po(1,1,3) is u = i+ ( Dj+ k.

Q: Two cars start moving from the same point. One travels south at 16 mi/h and the other travels west a...

A: Given: Two cars start moving from the same point.One travels  south at 16m/h and the other travels w...

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A:

Q: (a) Find the 3rd degree polynomial whose graph is shown above. In other words, find the constants. (...

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts f...

Q: Find an equation of the tangent line to x^2y^3 −y^2 +xy−1=0 at (1,1).

A:

Q: 9. S e*(3 – 2e?)²dx

A:

Q: Factor the difference an+1 – an to show that the given sequence {an} is strictly increasing or stric...

A:

Q: Title: Differentiation Rules Tasks: Solve the following problems completely and accurately. Use the ...

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want...

Q: A firm produces two types of graphics calculators, x hundreds of type A and y hundreds of type B per...

A:

Q: Find the general term of the sequence, starting with n = 1, determine whether the sequence converges...

A:

Q: Σ k! k=1

A:

Q: Use the limit comparison test to determine whether the series converges or diverges. 8k2 – 6k + 6 16...

A:

Q: Application of the derivative: I. Find the slope of the following curves at the indicated point. 2. ...

A:

Q: Consider the function f(r) 7x + 4z . For this function there are four important open intervals: (-00...

A: critical numbers are those such that value of the derivative of the function is zero.

Q: 5. The expression (x + 3)? is equivalent to: A) x? + 6x + 4 B) x? + 4x + 9 C) x? + 2x +9 D) x? + 6x ...

A:

Q: 7. An open rectangular box having a volume of 9 m is to be constructed from a tin sheet. a) Show tha...

A:

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Analysing the sequence we can see: Numerator of the sequence is 9 in every term.            Numerato...

Q: . Antibiotic treatment. A biologist has a colony of a toxic strain of bacteria that covers 500 mm² i...

A: We have to find the area of the bacteria coloney as a function of time at the gives instances.

Q: To evaluate the / sin-(x) + sin(x) cos2(x) -dx using basic formula of integration (without using sub...

A: We need to find values of f(x).

Q: Use any method to determine whether the series converge. 00 19 (a) > EI Vk + 1 This series * cos () ...

A: (a) The given series is: ∑k=1∞19k+1 Let, ak=19k+1, k≥1  

Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point (2...

A:

Q: Evaluate by any applicable method. S sin (y) cos" (G4) dy None of the choices. Please refer to my so...

A:

Q: following questions. (Let each square along the horizontal axis represent 90°. Let each square 2. Gr...

A:

Q: – ydx + (x ++ Vy )dy = 0

A: Given that Diffrancial equation-ydx+x+xydy=0Solution:-ydx+x+xydy=0x+xydy=ydxdxdy=x+xyydxdy=xy+xyydxd...

Q: +o0 S 13 In n n=1 Determine whether the sequence converges, and if so find its limit. If the sequenc...

A:

Q: quantities

A:

Q: Find the area of the region that lies under the graph of f over the given interval. Please solve usi...

A: Topic:- application of derivatives

Q: (In 10x+4lnx) "dx Identfy the correct u A Inx B In°x+4 In x

A: topic- definite integral

Q: )

A:

Q: (F+2)y+(F-12)x+2z 3. Draw the graph of the linear equation: = 4z + 7. %3D (K+2)

A: Solution is here

Q: Find K, B and r for H.W Find K, B and T for 1. r(t) = (3 sin t)i + (3 cos t)j + 4tk %3D 2. r(t) = (c...

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the remain...

Q: (nx)dy/dx+2y=xy^(n+1) where n is constant, solve using linear equation diff eq

A:

Q: If a linear function has the points (4,1) and (9,9) on its graph, what is the rate of change of the ...

A:

Q: " sin²(x) + sin(x) cos²(x) To evaluate the -dx using basic formula of integration (without using sub...

A:

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the ...

A:

Q: find the go th deriva yive of Y= (08 3x

A:

Q: " sin²(x) + sin(x) cos²(x) To evaluate the -dx using basic formula of integration (without using sub...

A: ∫sin2x+sinxcos2xdx = ∫sinx(sinx+1)1-sin2xdx                               = ∫sinx(sinx+1)(1-sinx)(1+...

Q: Showing all steps show why the differential of Tan (x)is equal to sec? (x) (f) Question

A: Given problem:- Showing all steps show why the differential of Tan (x)is equal to sec²(x)

Q: y'=y/x-cot(y/x) solve using homogeneous equation (diff eq)

A:

Q: Functions f and g are defined by g(x) = v-x+4, x<4; X e R h(x) = 2e*, x20; xe R (a) Find the composi...

A:

Q: A trapezoidal trough is 10 ft long, 4 ft wide at the top, 2 ft wide at the bottom and 2 ft deep. If ...

A:

Q: (d) Find the coordinates of the inflection point. Hence state the intervals for which the curve is c...

A: A graph is given in the questionx-intercepts: -1,0, 1,0, 2,0y-intercept: (0,1)

Q: sect tan³Od0 cos® tane B sec® sec²0 D cose E None A)

A:

Q: k=1 1) Your answer is incorrect. Try again. This series can be rewritten in which way? 43 7 k=1 k-1 ...

A:

Q: calculate af fe and ду

A: ∂ ∂ xxyx2-y2x2+y2

Q: 8. (x + 2y – 1)dx + (2x + 4y – 3)dy = 0 (r - 1)y' = v+ 2(x – 1)3 9

A:

Q: t(dx/dt)=6te^(2t)+x(2t-1) solve using linear equation

A:

Q: ,2 + 5х + 4 f(xæ) х — 1

A: For x-intercept substitute f(x)=0⇒x2+5x+4x-1=0⇒x2+5x+4=0⇒x2+4x+x+4=0⇒x(x+4)+1(x+4)-0⇒(x+4)(x+1)=0⇒⇒x...

Q: When you evaluate: dx, The sum of the coefficient of X for any constant n is

A:

Q: (b) Find the volume of the region D bounded in back by the plane r 0, =0, 1-y, on the top by the par...

A:

Q: PROBLEM 1 Pis known to have a value equal to 250 Ibs. Using rectangular components, determine (a) th...

A: