Find all relative extrema and saddle points of the function f(x, y) = −2x4y4 . Use the Second Partials Test where applicable.

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: The given integral is ∫04p9+p2dp. Let x2=9+p2. This gives  2x dx=2p dpxdx=pdp. when p =0,  x=3. when...

Q: Solve the initial value problems d2y/dx2 = 2 - 6x; y'(0) = 4, y(0) = 1

A: We have to solve the initial value problem: d2ydx2=2-6x; y'0=4,  y0=1 Integrating both sides, ∫d2ydx...

Q: The graphs show that the three components of love, namely, passion, intimacy, and commitment, progre...

A: Given interval: x| 7<x<9

Q: Evaluate using Partial fraction method S X-7 Jx+ 4)(x² + 9) ° xp-

A:

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral     sin 6 2 x ...

A: Consider the given:∫sin62x dx Apply u-substitution:  2x=u∫sin62x dx =∫sin6u12du=12·∫sin6udu

Q: Verify the identity:( tan θ cot θ) /csc θ= sin θ.

A: We have to verify the identity: tan θ cot θcosec θ=sin θ We know the formula of trigonometric functi...

Q: Use integration tables to find or evaluate the integral ∫ 1 / sin   x cos   x dx

A: We have to evaluate the integral: ∫1sin x cos xdx We know the identity: sin2x+cos2x=1 Substituting t...

Q: Differentiate the function. (2x- 1)

A: Given:y=12x-15

Q: You commute to work a distance of 40 miles and return on the same route at the end of the day. Your ...

A: From the given, the average rate return trip is 30 miles per hour faster than your average rate on t...

Q: Graph the given square root functions, f and g, in the same rectangular coordinate system. Use the i...

A: fx=x When x=0, f0=0=0 When x=1, f1=1=1 When x=4, f4=4=2 When x=9, f9=9=3 Therefore fx=x passes throu...

Q: Define even eigenvectors?

A:

Q: Solve the linear system using Gauss-Siedel Method with x = y = z0 = 0 to approximate the solution. I...

A:

Q: Find all numbers that must be excluded from the domain of  rational expression. [13/(x + 9)]

A: We have to find the numbers that should be excluded from domain of rational expression: 13x+9 We kno...

Q: Find the derivative of the following function. y= -87x2 -9 dy 口 dx

A:

Q: Rewrite expression without absolute value bars. |12 - π|

A: Rewrite expression without absolute value bars.  |12 - π|

Q: Find the limit of the following sequence or determine that the sequence diverges. {((-1)n)/(2n)}

A: To Find  The Limit of −1n2n

Q: Given nonzero vectors u, v, and w, use dot product and crossproduct notation, as appropriate, to des...

A: Projection of vector u onto v will be: Projvu=u→·v→v→ Therefore, Projection of vector u onto v is gi...

Q: Trigonometric substitution x = tan 0, dx = sec20 d0

A: We have  x=tan θ Differentiating both sides with respect to θ, dxdθ=d tan θdθ=sec2θ Since, derivativ...

Q: For what values of rFor what values of  y = e rx   satisfy the  equation   y " + 5 y ' - 6y=0

A: y''+5y'-6y=0 Let, y=erx⇒y'=r·erx⇒y''=r2·erx Therefore given differential equation becomes, y''+5y'-6...

Q: While integrating[(x² – 3 ) Inx dx by integration by parts we get the value of v = a. 1 O b. x2 - 3 ...

A: Solution: Given ∫x2-3lnx dx

Q: Suppose the demand function for x thousand of a certain item is p = 140 + where x>1 and p is in doll...

A: Given :-  Suppose the demand function for x thousand of a certain item is p = 140 + 80ln x , where x...

Q: Show that f(t) dt ) dx (x - a)f(x) dx.

A: To prove: ∫ab∫xbftdtdx=∫abx-afxdx  

Q: Evaluate the following integrals.

A: We have to solve the following integral ∫3x2+3x+1x3+xdx Now, we will solve this by partial fraction ...

Q: Determine the validity interval for solving the initial value problem

A: Solution: The objective is to find the solution of the given differential equation

Q: Use the definition of a derivative to find f'(x) and f"(x). Then graph  f, f' , and f" on a common s...

A: Given function is fx=x3-3x. Power rule of differentiation states that: ddxxn=nxn-1 Differentiating t...

Q: Answer the following True or False: If lim f(x) exists, then f(x) is a differentiable function at x ...

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Q: | cos(x) sin(2x) dæ

A:

Q: Solve  y"-9y'+14y = 0

A: We have to solve  y" - 9y' + 14y = 0  (D2 - 9D + 14)y = 0 The auxiliary equation is  m2 - 9m + 14 = ...

Q: Suppose a + 0 is any real number. (a) In the expression a", which is the base and which is the expon...

A: Given: a≠0. (a). In the expression an base is a and exponent is n.   (b). If n is positive integer t...

Q: Differentiate.  y =t / (t- 1) 2

A: To differentiate the function y=tt-12. Quotient rule of differentiation states that: ddxuv=vddxu-udd...

Q: Q3(a) Solve the following system of simultaneous linear equations using Gauss-Seidel method 5x, – x2...

A: The given system of equations is as follows. 5x1-x2=9-x1+5x2-x3=4-x2+5x3=-6 Rewrite the above equati...

Q: Use the given graph to solve the following; a. Determine the function’s domain. b. Determine the fun...

A: The graph of function y=fx is shown in the figure. (a) The domain of the function can be found where...

Q: CHAP 7: PARTIAL DIFFERENTIATION OF FUNCTIONS Exercises Find the critical points of the functions. Fo...

A:

Q: Verify the identity: (csc t - 1)/cot t = cot t/(csc t + 1)

A: Verify the identity: csc t-1cot t=cot tcsc t+1

Q: Find div F and curl F. F (x, y, z) = 5e" i – 7 cos y j+3 sin´z k -

A:

Q: Evaluate using Partial fraction method 5x² +27x + 12 dx -dp- x² – 5x +6

A: Here, the integrand is not proper rational function, so, we divide 5x2 + 27x +12 by x2-5x +6.  

Q: Assigning a value to

A:

Q: sin9x Evaluate lim x +0 8x O a. 0 O b. -9 8 О с.9 O d. 9 8

A: D option

Q: Solve the system:

A: we have to solve the given system of equation 5x-2y=4 -10x+4y=7

Q: Calculus Question

A: Direction Derivative:Direction derivative is a rate of change of any function at a given point.It is...

Q: 72. Transformations The graph of f is given. Draw the graphs of the following functions. (a) y = f(x...

A: NOTE- As we are allowed to answer three subparts per question in a single session so, i have solved ...