Calculate the gradient of h(x, y, z) = x z

Q: Suppose z = f (x, y), where x (s, t) = 2st and y (s, t) = s t + 7. af af At point P, suppose = 3 and…

A: Here we have to find a partial derivative at a point.

Q: x4 Lz²+9dx 3x³ +9x−27 tan- ¹ (-) +C Option 1 x³ − 9x + 27 tan−¹ (3) + C Option 3 3x³ + 9x 9x + 27…

A: Here Is the solution

Q: Find the k-component of (curl F) for the following vector field on the plane. F = (Xex)i + (8y ex)j…

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

A: To find equation of tangent line and then arc length of thegivencurve.

Q: Determine the magnitude of the vector difference V' = V₂ - V₁ and the angle 0x which V' makes with…

A: We have to find the vector and angle.

Q: 1. Be the data set according to the following table of values: On a coordinate plane, plot the data…

A: topic- exponential function

Q: 8+6.4+5.12+... Which one of the following is the sum of this infinite series? a) 40 b) 35 c)…

A: topic- geometric series

Q: Eliminate the parameter t to find a Cartesian equation in the form * = f(y) for: [x(t) = −2+² ly(t)…

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Q: A gas station sells Q gallons of gasoline per year, which is delivered N times per year in equal…

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Q: Evaluate f(x³ -x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

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Q: X=(1)+ wam (xf pulf Z-x7=(x)₂ + £I-E#

A: Topic = Integration

Q: Which of the following graphs is the correct plot of y = 5+ 5 4 4 -3 3 2 2 -1 + 5 6 2 4 -1 -2 --3-…

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Q: √ /1 + x² dx

A: We can solve the integration as below.

Q: What is the 6th term of (x - 1)¹0?

A: Given problem:- what is the 6th term of (x-1)10

Q: Solve it neatly, correctly, and comprehensively.  2. An open box is made from a thin sheet of…

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

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Q: Confirm by multiplication that x is an eigenvector of A, and find the corresponding eigenvalue. 301…

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Q: Use the Fundamental Theorem of Calculus, Part 1 to find the derivative: d •√x (t² + Int)dt dx Sa

A: First I have written the Fundamental theorem of Calculus and using it for given problem and find the…

Q: 2x²+3x+1 x-1 f(x)=3

A: Given problem:-

Q: ¹In(1 + x) -dx X

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Q: Find the general Solution of the complement OF the following differential equation y"-7y) -6y=013…

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Q: S eln (1-t) 1-t - dt ed to you in any form

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Q: Use Cartesian coordinates to evaluate JIJ y² dv 2 D where D is the tetrahedron in the first octant…

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Q: Question 2 Use Euler's method with step length h = 0.5 and determine an approximate value for y(3)…

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Q: Without using a calculator, compute the sine and cosine of 210° by using the reference angle. What…

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Q: S 7. Evaluate 8. Evaluate 9. Evaluate (cos x - sin x) dx cot²x dx (sin x + x) dx

A: Given problems:- Solve the following using the theorems on differentiation. 7. ∫ (cos(x) -sin(x) dx…

Q: In Exercises 1 and 2, compute the solution of the given IVP. d²y 1. +9y2 cos(3t), y(0)=2, y'(0) = -9…

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Q: # ZZ Convert the following equation in Cartesian (rectangular) coordinates into the equivalent…

A: Use trigonometry function

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

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Q: 3) Evaluate f (xy + 2z)ds. C is the line segment from (1,0,0) to (0,1,1).

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Q: Let 1 5-1 A = 0 1 0 and P = 0 0 0 15-2 05 Given that P diagonalizes A, then compute A¹¹. i A" i i

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Q: f' f" 1 I I 1 I 1 I I 1 A A B D B D y C E D E

A:

Q: Analyze and sketch:  x- and y-intercepts  Critical Numbers  Table for increase/decrease + local…

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Q: The surface parametrized by 7(u, v) = (u, v, u - 2v) is a plane O a hyperboloid a cone a cylinder

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Q: In f(x) dx = F(x). F(x) is called the

A: follow the procedure given below.

Q: Find a vector equation for the plane that contains the points P, Q and R Find a scalar equation for…

A: Given points: P(2,1,1),Q(0,4,1),R(−2,1,4) and S(1,5,−4) Equation of a plane in cartesian form…

Q: Use Cartesian coordinates to evaluate JJ v² av where D is the tetrahedron in the first octant…

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Q: S dx √4x² - 49 x > 7

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Q: 4. Evaluate the double integral: y f. L y¹/3 x7 +1 (Hint: Change the order of integration to dy dr.)…

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Q: estion 9 s triple integral represents the volume of a cylinder. True False V = f²" f²f³ r dz dr do

A: To evaluate the triple integral.

Q: hand written plz 5. Let D be the region bounded by the lines y = x, x=3 and the curve y = (a) Sketch…

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Q: Integral Evaluate the √x (x-²) ³ dx

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Q: Solve the given differential equation. All solutions should be found. (3y² + 2xy) dx − (2xy + x²) dy…

A: A detailed solution is given below.

Q: da d²y +6- dx dx² + 11 dx+6y = ex + cosx бу

A:

Q: 6) Approximate √²³|x² −1|dx with a right-endpoint Riemann sum using four equal subintervals.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 7) Use the double integral of a cross product to find the surface area of x = z² + y that lies…

A: Let's find surface area  by using double integral.

Q: The region D bounded by y=0, x=y - 1, X x = as given in the following figure. YA 3.0+ 2.5- 2.0+ 1.5+…

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Q: 1. y ecos(-2x) =

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Q: Find lul, Ivl, 12ul, |2v|, lu + vl, lu − vl, and _|u| - |v|. u= 5i + j, v = 2i - 4j

A: We need to calculate the magnitudes of given vector and evaluate the given expressions.

Q: 7) Suppose the population of Detroit was 1.5 million in 1990 and 1.0 million in 2002. If the city is…

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