Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

Q: 7. Use integration tables to find or evaluate the integral. (Use C for the constant of integration.)…

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Q: (18) Find the derivative of the functio 2²+5 3 Y=2²-5 Nor me it to Vitou inst

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Q: Find the volume of the solid generated by revolving the region bounded by the curves 3π y = sin x +…

A: Given problem:- Find the volume of the solid generated by revolving the region bounded by the curves…

Q: 4. What are the values of A, B, C, and D so that 1 a. A = b. A = C. A = d. A = HALA00 B= C= B B 1 8'…

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Q: (14 Find the derivative of the function 7 (^ Y = x²+3 15 x²-3

A: Find the derivative of the function  y= [(x2+3)/(x2-3)]5

Q: Let S be the plane with equation 2x - 3y + 4z = 1. Find parametric equations of a line that goes…

A: Explanation of the answer is as follows

Q: The area of an ellipse with axes of length 2a and 2b is given by A = Tab. Approximate the percent…

A: Concept: We have given the Area A=πab Here the length a is increasing by 2% which is daa=2% Here the…

Q: Calculate the double integral. 7x S₂ x ² + x²0² +y dA, R= [1, 4] x [0, 1]

A: Explained below

Q: Determine whether the series is convergent or divergent by expressing the nth partial sum s,, as a…

A: We use Series integral method to find whether the series is convergent or divergent.

Q: 4. At which points does the function f have absolute maximum or minimum, or local maximum or…

A: We have to find the absolute minimum, absolute maximum, local minimum, and local maximum.

Q: 16. Determine whether the statement is true or false. If it is true, explain why. If it is false,…

A: The solution is given below

Q: af The partial derivative evaluated at P is 6. əx Find the directional derivative of f at P in the…

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Q: S 4x+1 4x² + 2x + 1 dx In 14x² + 2x +1| + C Option 1 In 14x² + 2x + 1] + C 2 In 1 4x² + 2x +11+ C…

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Q: [4x 4x csc (4x) cot (4x) dx =

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Q: lim f(x) = 5 and_lim_f(x)=5, but f(3) does not exist. X-3 X-3* What can you say about lim f(x)? X-3…

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Q: Simplify. 2 sec 2 X 2 - 1

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Q: Question 3 [ For the system of linear equations -3x + 5y = 4 ny + 12x = -16 a) [: Find the values of…

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Q: If the terminal side of angle A goes through the point (−24/25,7/25) on the unit circle, then what…

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Q: Find Y'and y" Y = sin (x²) Y = 2x² cos (x²) 2 y" = ? 2

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Q: 3y What is the equation of the curve that passes through the point (1, 3) and has a slope of ○ y =…

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Q: Choose the direction vector for which the function f defined by f(x, y)= sin(5x) cos(3y) has the…

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Q: Solve the given differential equation by undetermined coefficients. y" - 8y' + 20y = 100x² - 91xex…

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Q: S." (inx+4)" x dx

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Q: The cost of fuel per hour for running a ship is proportional to the cube of the speed and is P1,350…

A: The given problem is solved below in detail.

Q: 4. Solve for 1 [(ax)²-b²]³/2 J dx.

A: See this solution in below.

Q: defined on the interval [-5, 7]. a.) f(x) is concave down on the open b.) f(x) is concave up on the…

A: This question can be solved using the concept of point of inflection, critical point and point of…

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 8xe…

A: The given function,  z=8xey-12ye-x

Q: Find the general solution to: dy X xẩy = xảy x²y d y = o y = Cet² ° y = Cezx² ○ y = ex² ez x² + C…

A: We need to find out the general solution of the differential equation.

Q: The acceleration of a particle is given by a(t) = (2t, 3, et). If the velocity at time t = 0 is…

A: Given: Now, the velocity will be           v(t)=<∫2t, ∫3, ∫et>      =<t2+c1, 3t+c2,…

Q: -1 xp(x + 1)zz² J

A: The given integral,        ∫-11e2x1+xdx

Q: Choose the normal vector of the tangent plane to the surface defined by Z = e6x²+14xy-5y² at the…

A: To find: The normal vector of the tangent plane to the surface at the given point. Given…

Q: (a) lim x² - x + 6 X2 x 2 x² + 2x - 3 x² (b) lim x - 6 x 3 x² - 2x - 3 x - 4 (c) lim x+4√√√x-2

A: a.limx→2x2-x+6x2+2x-3=4-2+64+4-3=85b.limx→3x2-x-6x2-2x-3limx→3x-3x+2x-3x+1limx→3x+2x+1=54

Q: dp dt Suppose that the current population is 100,000. (a) What is the predicted rate of growth 3…

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Q: Suppose a. ® Г f(x)dx = 36, [ f(x) dx f ' = f(x)dx = 12,

A: The given integral values,    ∫09f(x)dx=36 and ∫79f(x)dx=12

Q: 15. Show that the equation, 2³ + e* = 0 has exactly one real root.

A:

Q: 18. if f(x) = 2x² + 3x² - 4x-5 X+1 Suggested Table X f(x) -1.1 -1.01 -1.00 find X-7-1 f(x) = ?…

A: The given function,  fx=2x3+3x2-4x-5x+1

Q: Consider the graph of the function f(x) given on the next page, which consists of line segments and…

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Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare…

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Q: 013 Verify that the function satisfies the two hypotheses of Mean Value Theorem on the given…

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Q: Explain whether or not the Quotient Rule should be used to find the partial derivative. Do not…

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Q: sint F(x) = √"* ( *ª*** ( √ ¹ + uª) du) dt Jo

A: The Fundamental Theorem of Calculus says: F(x)=∫ag(x)f(t) dt⇒F'(x)=f(g(x))g'(x)

Q: (2) Use a known Maclaurin series to obtain the Maclaurin series for f(x) = sin²x. (Hint: Use sin²…

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Q: Find fx and f, and evaluate each at the given point. an(1), (6, -6) f(x, y) = arctan fx(x, y) = (No…

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Q: Answer the following questions for the function defined on the interval [-5,7). a.) f(x) is concave…

A: Use derivative concept

Q: and & and ß are between 0 and f/2. 3

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Q: dx Evaluate So x²+4

A: Follow the procedure given below.

Q: Find the derivative of y with respect to the independent variable. y = 2ln 2t 2 In 2 t OB. 2In 2t In…

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Q: Express the following as a linear combination of u =(3, 1, 6), v = (1, -1, 5) and w = (4, 2, 4).…

A: To write down the vectors into the linear combination of the given vector.

Q: ections at the given point

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Q: The distance from the ground of a person riding on a Ferris wheel can be modeled by the equation d =…

A: Follow the procedure given below.