4) Value of gold bar is V=2500 evt and interest rate r=0.07 please find the optimal value of t to maximize the present value. Show both first and second-order conditions.

Q: Find div F and curl F if F(z, y, z) = 9e#i-9 cosyj+3sin? z k. %3D div F = curl F=

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Q: 4 4 4 + + 9. 27 3 +

A: Given problem:- (4/3) +(4/9) +(4/27) + ........  Determine whether given  geometric series…

Q: 7. lim vx² + x + 1 – vx² + 1 X00

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Q: 2) Evaluate the integral S inx dr 2.

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Q: dy 4 + 4y = xe'

A: To solve the differential equation by using method of undetermined coefficients.

Q: II. INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) F(x) f'(x) F'(x) lim = lim…

A: To evaluate the given limit of the function.

Q: 3. lim (cscx –- cotx) x0+

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Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: Here,  0≤x≤4-yy≤z≤8-y0≤y≤4 To change the order of integration to dx dz dy to dz dy dx

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Q: 13) Determine the lim X--9 + 169 く+9

A: Since the student has posted multiple questions and does not mention any specific question, so we…

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). 3 ||r(t)||³ r(t) = 3 cos(2t)i+ 3 sin(2t)j + tk…

A: The given formula is: κt=r't×r''tr't3 And rt=3cos2ti+3sin2tj+tk   As we know that; The Chain rule;…

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Q: Solve the differential equation Integrating Factor by Linear Equation: (xy² + x²)dy + xydx = 0 %3D

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Q: Н.W (1) Solve the following differential equations of dy 2 - - (1+y*)e* dx 1- ye** . dy = dx; x+y…

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Q: Find the particular solution of the DE y " -11y + 24y = 0 subject to the boundary conditions y (0) =…

A: Given y''-11y'+24y=0  ; y(0)=2  and  y'(0)=-3

Q: Qs show that : sinh CA+B) = SinhA. coshB + Cosh A. simhB

A: This question is related to Hyperbolic functions, we will solve it using given information.

Q: 2 Find the cartesiun equation for the polar Carre rこlcos . Al(x-2)²+y2=4 ty²-4 %3D c)x²+ Cy-2)?=4 D)…

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Q: 3n4 Σ Consider the series > 6n4 + 2 n=1 Based on the Divergence Test, does this series Diverge?…

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Q: Find div F and curl F if F(x, y, z) = 3e™Y i– 3 cos yj+ 10 div F=

A: Given: 3exyi-3cosyj+10sin2zk

Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: ind the arc length oI the parametric curve. 0 = 6 cos (t), y = 6 sin(t), z = 8t; 0 stST

A: Given: x=6cost, y=6sint, z=8t

Q: Find the limit. NOTE: Enter the answer using round brackets. t? +9 1 lim t+oo 3t2 + 4' 6t = (?, ?)

A: 1/infinity=0 is used

Q: 2. Determine the area of the region bounded by the curve y = x3 – x2 – 2x, and а. the x-axis

A: Given:    a)   Curve y=x3-x2-2x Curve cuts the x-axis at           x3-x2-2x=0           xx2-x-2=0…

Q: Question 15 Find the curvature k and radius of curvature R for the curve at the given point. y = sin…

A: The given curve is y=sin2x we have to find curvature and radius of curvature for the curve at the…

Q: 1. If = (1.0.-3) and i = (6,-3,-4) compute ixw.

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Q: 7.) L13x + 1|dx

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: True or False. Explain your answer The limit of sin(x) as x approaches very large values is 0 or 1.

A: Given

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5…

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Q: E(-1)" n n=1

A: Series

Q: Solve the differential equation Integrating Factor by Linear Equation: dx + xcoty = ecosy dy

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Q: Solve the area bounded by the curve y = 4x - x² and the lines x = -2 and y = 4.

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Q: Solve the following differential equations of e • dx+2(xe" – y)dy = 0;

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Q: Find curl (7z i + 8x j + 9y k). curl(7z i + 8x j + 9y k) = ( i )i + ( i )j + ( i )k

A: This question is related to vectors, we will solve it using given information.

Q: 19. dr V4-a 20. dr 21. 2)

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Q: Find the area bounded by the curve x = y² + 2y and the line  x = 3.

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Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: Integral

Q: Determine the vector field of F. F(x, y) = yl – x) 1.

A: Vector field

Q: Follow the instructions. Typewritten for upvote. No upvote for handwritten. Thank you

A: We have to find the number

Q: dz 14. Evaluate S z(4+2)

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Q: 2. SET-UP the definite integral that will give the area of the region specified using (a) x as the…

A: Area

Q: Evaluate the values of x, y and z of the three equations three unknowns : 4x - 2y + 6z = 8 2x + 8y +…

A: Given: 4x-2y+6z=82x+8y+2z=46x+10y+3z=0

Q: Evaluate the double integral. 5x (4 + y)¯² dA; R R is the region in the first quadrant enclosed by y…

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Q: 2. lim (e* – 1)lnx

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Q: I. Evaluate the following antiderivatives. tan (VT) + 2 1. TE (sec(/r) – cos(/#)) dx Cos(V))

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Q: dy_ y -1 dx

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Q: 1 1 + 25 1 +. 125 Given the series 1+ Does this series converge or diverge? converges O diverges If…

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Q: 1 +1 dz 7. Ji Vz -1

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Q: Find the indicated limit or state that it does not exist. x2y + xy2 lim (x, y)-(0, 0) x2 + y2 O 2 O…

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Q: NOTE: Enter the exact answer. xe*y dy dx

A: