Question a) b) Let f(x, y) = 2√x - y²e-2xy Find fx and fy. Evaluate fxxy(4,-1). + NIA

Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² H in the…

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Q: Find the angle of inclination of the tangent plane to the surface at the given point. x² + y² = 5,…

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Q: A dam has a semi-circular gate at the bottom that is 4 m in diameter. The dam is 12 m high and…

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Q: Choose the correct answer for the following function: f(x, y) = cos(2x²y³) Select one: None of the…

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Q: Use the given information to find the exact value of the trigonometric function.  sin θ = 1/4 , θ…

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Q: Solve the following initial value problem: y(t) = = dy dt +0.9ty = 6t, y(0) = 1

A: Given: dydt+0.9ty=6t,      y0=1

Q: lower sum upper sum Function f(x) = 9 - 2x s(n) = S(n) = Interval [1, 2]

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Q: The solution was wrong. What is the correct solution?

A: Solve the following

Q: Question 23 Find the length and width of a rectangle that has an area of A square centimeters and a…

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Q: Find the gradient of the function at the given point. In(x²-y)-3, (3,8) X Vz(3, 8) = z =

A: The given function,   z=lnx2-yx-3, at the point 3,8

Q: L 2x²³ + 8x doc 3 √x² + 4

A: This question can be solved using the concept of integration by substitution.

Q: What is f (x) of f(x) = 320 (2x-7)³ O4x²-28x-31 (2x-7)¹ [(8x-28)-4(4x²-28x-31)] (2x-7)¹ O4x²-28x-31…

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Q: Given that the graph of f(x) passes through the point (5,10)( and that the slope of its tangent line…

A: Given , The graph of f(x) passes through the point (5,10) and that the slope of its tangent line at…

Q: Find the area of the triangle with vertices P(1,3, —5), Q(0, 0, 0) and R(4, 5, 1). NOTE: Enter the…

A: The triangle with vertices P1,3,-5, Q0,0,0 and R4,5,1

Q: Find y': Oy: Oy = Oy' = O y' y cos(xy)+1 x cos(xy)-1 x cos(xy+1) y cos(xy)-1 y cos(xy)+1 x cos(xy)-1…

A: To find the value of y' for the given function.

Q: A movie theater has a seating capacity of 163. The theater charges $5.00 for children, $7.00 for…

A: A detailed solution is given below

Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

A: This question is based on the general term of geometric progression.

Q: What is the integral of f cos¹ (2t)dt? Ot+sin(4t) + sin(8t)] + C None of the choices cos" (2x)…

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Q: f the measurement of the side of a cube is increased from 5 cm to 5.2 cm, the approximate increase…

A: Side of cube is increased from 5 to 5.2

Q: EV None of the choices Ocot³ (1)-cot (1) - ○tan³ () - tan() Ocot³ (¹)-tan (1)

A: givenI=∫cot4(1θ)θ2dθlet  1θ=x-1θ2=dxdθ1θ2dθ=-dxI=-∫cot4(x)dx…

Q: Calculate the integral where R is the region inside x ^2 + ?^ 2 = 4? and external to x ^2 + ? ^2 =…

A: We have to calculate the integral.

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = X, (1, 2, 2) Xx…

A: fx,y=yx, 1,2,2

Q: Find the derivative of y = arccos x + x 1-x²

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Q: z = (x + y)², x = s²t, y = st². Use the Chain rule to find d ds for t = 1 and s = 2.

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Q: What is the equation of the tangent live the When X = 4 √(x) = ² -6√x cheve f(x) = 3/

A: Given ::fx=8x-6xx=4

Q: The function f gives the weekly profit, in thousand dollars, that an airline makes on its flights…

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Q: dz Evaluate: ¹5 102 -5 0 1 O Divergent 00 O-1

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Q: If the given sequence is a geometric sequence, find the common ratio. 4/3, 8/3, 16/3, 32/3, 64,3

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Q: Choose the correct answer for the following limit: Select one: Ο Α. 0 O B. Does not exist. OC. None…

A: According to question,Given Limit,Let l = limx, y→0, 0x3 + 6y25x3 + y2

Q: 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1, -1). 2. Find the…

A: Given :fx,y,z=lnxy-zx2

Q: if: z = cos 0+isin prove that: 1) 2+1 z+1 2)221 +1 = itan 0 z² = Z

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Q: The integral fe*- a dxdy is equal to O 2e-a+2 2 2e-a-4 2 2e-a+4 2 2e-a 2 9

A: Given :∫01∫0yex-adxdy

Q: f(x, y) = x²y + 4y and x = st, y = 2t - 3s. af and off. af Use Chain Rule to find ds Write your…

A: Follow the procedure given below.

Q: A dam has a semi-circular gate at the bottom that is 4 m in diameter. The dam is 12 m high and…

A: Given data as follows :- Diameter of the semicircular gate is 4m. Height of the dam is 12 m.  Water…

Q: The figure has a tangent line drawn at a labeled point. c(t) thousand chips 8 6 4 2 (1.95, 7.07 0.5…

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Q: Find the point(s) on the surface at which the tangent plane is horizontal. z = 3x² - y² + 4y ) (x,…

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Q: Given the function of two variables f(x, y)= ln(√x + 16). The partial derivative with respect to x…

A: Given, f(x,y)=ln(x6+y66)

Q: -(4x³y - 16)dy = (6x²y² – 10)dx. A) Show that the differential equation is exact. B) Solve the…

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Q: Evaluate (In x)³ dx

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Q: Evaluate cosh² x dx }(sinh2n +2) + 0 +x + C O2e²x +4z + C 8 O None of the choices cosh(z)sinh(2)++C

A: We can solve this as follows:

Q: The limit exists and is equal to 0. Select one: O True O False lim (x,y) →(0,0) 36x²+25y² 6x+5y

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Q: S dz zlnz (Inz)²-1 Select one: O A. Q B. O C. Q D. arcsec(Inx) + C arcsin(lnx) + C arccot(Inx) + C…

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Q: A polynomial f(x) and one or more of its zeros are given. f(x)=x²-8x³ +95x² +16x-194 4-9i is a zero…

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Q: Calculate the volume of the solid bounded by the surfaces given by x2 + y2 = 1, z = 0 and z= x2 + y2

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Q: Solution is incorrect. Please correct it.

A: dydx=6y18+9x2y18⇒dydx=6y18(1+9x2)⇒y18dy=6(1+9x2)dx

Q: If z = x - 2y, dz and x = 2t, y = 5t, then the value of dt Select one: True False at t = 3 is equal…

A: Here, the given functions are: z=x-2y,x=2t, y=5t⇒z=(2t)-2(5t)⇒z=2t-10t⇒z=-8t

Q: Evaluate the limit: limo* [cos(3x)]= O e-3 03 e 01 ◄ Previous

A: To evaluate the limit.

Q: The annual number of passengers going through Hartsfield-Jackson Atlanta International Airport…

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Q: What is the value of k so that the function f(x) is continuous at x=2 O-3 O - 3/2 1/2 0 1 T-2k f(x)…

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Q: A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate…

A: topic- application of derivatives