Q: Find both first partial derivatives. Z = cos(4xy) %3D Oz %3D ду
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Q: Q2) Find the integral of: f*,6 tan*x dx
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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…
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Q: Find curl (3z i+ 4xj+9yk). curl(3zi+ 4xj+ 9yk) = ( i )i + ( i j+( i %3D
A: We have to find the curl of the given vector.
Q: proportional
A: We will solve the problem.
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Q: Consider the following. w = xyz, x = s + 5t, y = s – 5t, z = st? (a) Find dw/s and dw/at by using…
A: Using chain rule and converting function in term of s and t are differentiated.
Q: . Evaluate the double integral , Sf(r,0) dA, and sketch the region R. 5. 2 S, v9– r² dr de
A: Let's find.
Q: Q2) Find the integral of: L*„6 tan*x dx 4
A: LetI=∫-π4π46tan4xdxTake the constant…
Q: e- + cos (xy) = (4 – 3z) (2 + 2.x), UIM 4. find ду ÚTM az cos (ху) — (4 — 32) (2- 8 UTM UT UTM
A: Partially Differentiate with respect to y
Q: 13 of 20 limz→-6 746 a+6 Does not exist 8.
A: Let's find.
Q: Find the area bounded by the given curves, axes and/or lines. 1. y2 + x – 4y = 5; y-axis
A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…
Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…
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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||³ r(t) = t’i+ t°j K(t) :
A: We have to find the value of k(t)
Q: e product (4 8 10 9)(2 7 6 11)(1 35 12)
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Q: o} (2xy+y?) dx - 2x² dy = O 2.) xy dx -(x + 2y)? dn
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Q: 12) Find the n-th term of the Sequence 12,8,4,0,-4,-8,..
A: nth term of the arithmetic sequence : an =a+(n-1)d , where , a-first term and 'd' is common…
Q: Let v=f(x) be a solution of the first order linear differential equation y'=y-10x² such that f(0)…
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Q: Use the formula k(t): |r'(t) × r"(t)|| to find k(t). r(t) = ti + t°j K(t) =
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Q: Describe the graph of the equation. r = 2 cos t i- 10 sin t j + k O An ellipse in the plane x = 1,…
A: Parametric plot÷
Q: Evaluate the definite integral. e16t i + e¬tj +t k )dt O el6 – 1 (e-- - 1) + i+ (e-1 – 1) j + , k 16…
A: To solve the given integral.
Q: Obtain the inverse transform of the following 2s-3 1. s2-9 10 (3s2+12) + (s²–25) 3s-2 3.…
A: As you have asked multiple questions so I have answered only first question as per the…
Q: Suppose that w = f(r, s, t), where r = r(x, y), s = s(r, y), and t = t(x, y). Which of the following…
A: Solution is given below:
Q: Solve the triangle. 5 B. A (Round to one decimal place as needed.)
A: On solving this we will get
Q: Use Disk Method only Find the volume of the solid formed by revolving the region bounded by the…
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Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…
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Q: 1. (1 + y?)° dy 2. S sin x+cotx dx sin?x
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Q: Calculate ri(t)· r2(t)] and ri(t) x r2(t)] first by differentiating dt dt the product directly and…
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Q: 3. a) Determine the slope of the function, h(x) = 4sinx at x =
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Q: Let T10 (x): be the Taylor polynomial of degree 10 of the function f(x) = In(1+ x) at a = 0. Suppose…
A: The possible value of x for which this approximation is within 0.001 of the right answer is 0 < x…
Q: 8. Evaluate the double integral ry=2x L3) dydz. x=1
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Q: (d) sec(x) – sec(x) sin²(x) = cos (x)
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Q: Would it be more difficult to find the points where there is a horizontal tangent line to this…
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Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…
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Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…
A: arc length
Q: Use the chain rule to find and , where as z = x² + xy + y, x = 6s + 9t, y = 5s + 8t %D First the…
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Q: dy when x = 1 is dx If y = e-ª In x then A) 0 B) Does not exist D) = E) e
A: We have to find the dy/dx at x =1
Q: a) Determine the position function, s(t), of an object if the acceleration is a(t) = 5t , (3) = 0,…
A: We know that a= dvdt, v= dsdt In particular, when velocity is positive on an interval, we can find…
Q: Use the properties of logarithms to expand the expression as a sum, difference, and/or constant…
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Q: Find two positive numbers that satisfy the glven requirements. The second number Is the redlprocal…
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Q: 4. S(9x + 33x +22) dx
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
Q: Solve using quotient rule: f(x) = (3x^2 – x + 4) (2x^2 – 1)
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Q: Find the volumes oF the solids geverated by revolving +he regions bounded by the graphs oF the…
A: Given:- the region bounded by y=2x2y=0 and x=2rotating about the x-axisusing washer/disk method…
Q: 4. x(x² – 1)² dx
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
Q: 3. a) Determine the slope of the function, h(x) = 4sinx at x =". b) Find the slope of the line that…
A: We can solve as follows
Q: What is the instantaneous slope of y == at z = 5?
A: for the instantaneous slope for a function f(x) at x=a we have to find f'(x) and then put x=a in…
Q: dzy What is dx2 for the curve given by x = t2 and y = t3?
A: Our Aim is to find d2ydx2 for the curve given by x=t2 and y=t3
Q: dy then dx If y = In(x/x² + 1), 2x2 + 1 C) x/x² + 1 2a2 +1 D) x(x² + 1) x² + x +1 E) x(x² + 1) 1 A)…
A: Find the derivative
Q: 1. Find fa(x, y) and fy(x, y) given f(x, y) = (csc y) Arcsin(r2).
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Q: Find the volume between the cone y = Vx² + z² and the sphere x2 + y² + z² = 25. volume =
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- How are the absolute maximum and minimum similar to and different from the local extrema?A particle moves on the line y = 2x + 1 in such a way that its x−coordinate changes at a constant rate of 4 units per second. A right triangle is formed by the vertical line from the particle to the x−axis, the line connecting the particle to the origin, and the x−axis. At what rate is the area of the right triangle changing when x = 4?Water is flowing at the rateof 6 m3/min from a reservoir shaped like a hemispherical bowl ofradius 13 m, shown here in profile. Answer the following questions,given that the volume of water in a hemispherical bowl ofradius R is V = (π/3)y2(3R - y) when the water is y meters deep. At what rate is the water level changing when the water is 8 m deep?
- Find volume between given functions about the y = -3 axis.How is derivatives utilized in solving for the dimensions and total area of a box?A tank initially contains 200 liters of brine with 20 kg of salt solution. Brine containing 0.25 kg per liter of salt flows into the tank at the rate of 3 liters/min, and the mixture kept uniform by stirring, flows out at the rate of 2 liters/minute. Determine the time when the concentration of salt becomes 0.15kg/liter.
- Suppose you are climbing a hill whose shape is given by the equationz= 1000−0.01x2−0.02y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (50, 80, 847). The positive x-axis points east and the positive y-axis points north. (a) If you walk northwest, will you start to ascend or descend? At what rate? (b) In what direction is the slope largest? Why?1 integrate using algebraic technique of variationWater is flowing at the rateof 6 m3/min from a reservoir shaped like a hemispherical bowl ofradius 13 m, shown here in profile. Answer the following questions,given that the volume of water in a hemispherical bowl ofradius R is V = (π/3)y2(3R - y) when the water is y meters deep. At what rate is the radius r changing when the water is 8 m deep?
- There is a tank in the shape of a paraboloid: Water is being pumped into the tank at a constant rate of 2π cubic inches per minute. If y denotes the water level, then the volume of water is given by V = πy2 / 2. (a) Suppose that the height of the paraboloid is 10 inches. Let a denote the rate of change of water level when y = 1 inch and let b denote the rate of change of water level when y = 5 inches. Without computing anything, do you suspect that a or b is greater? (b) Confirm your suspicion by explicitly computing a and bA bacteria population starts with 400 bacteria and grows ata rate of r(t) = (450.268) e1.12567tbacteria per hour. Howmany bacteria will there be after three hours?A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.1 cm/min. At what rate is the volume of the snowball decreasing when the radius is 11 cm