Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z)=x tan (2), (-8,-8, -8), v=-10i+7j+7k

Q: Find a power series representation for the function. (Center your power series representation at x =…

A: f(x)=15+x

Q: (a) Find a vector parametric equation for the part of the saddle z = xy inside the cylinder x² + y²…

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Q: Answer the following questions about the function whose derivative is f'(x) = (x - 2)²(x+3). a. What…

A: Given derivative of a  function as

Q: 23. Find the point(s) on the hyperboloid x² +4y² +2² = 84 where the tangent plane is perpendicular…

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Q: Find the values of x for which the series converges. (If the answer is an interval, enter your…

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Q: Let D be a parallelogram with vertices (0,0), (,1), (2.2), (2,3) Find a linear transformation…

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Q: 11 If f(1) = 10 and f'(x) > 2 for 1 < x <4 how small can f(4) possibly be? (Show your work)

A: If  and , then to determine the smallest possible value of .

Q: Let F = (4xyz + 7 sinx, 2x², 2x²y). Find a function f so that F = Vf, and f(0,0,0) = 0.

A: To find the function f such that F=∇f, we need to find the potential function whose gradient is…

Q: 3 Show that[sec(x)] = sec(z)tan(z) by writing sec(x) = cos(z) and using quotient rule. (Show your…

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Q: 7 A bacteria culture grows with constant relative growth rate. The bacteria count was 400 after 2…

A: Given:Bacteria count was 400 after 2 hours and 25600 after 6 hours

Q: 12. What value of k would give the function y = 15 sin(kx) a period of ? B. k=" = 7/ 5TT C. k= 6 A.…

A: To find the value of  that would give the function , a period of

Q: Find the following volume of revolution: y = x - x², y = 0, around the y-axis Volume: Find the EXACT…

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Q: Determine the intervals on which f is increasing or decreasing, assuming that given figure is the…

A: The graph of a function increases in the interval at which its first derivative is positive and the…

Q: Find the area cut out of the cylinder x² + ² = 100 by the cylinder x² + y² = 100.

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Q: 8 Two people start moving from the same point. One travels south at 6 miles/hour and the other…

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Q: either of the answer is incorrect.

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Q: Solve the initial value problem. ds 36t(9t²-7)³, s(1) 14 2 dt The solution is s =

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Q: Solve the system of differential equations. [6 - 13] ² 2 10 *1(0)18, x2(0) = 26 x₁(t) = x₂(t) =

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Q: Find div F and curl F if F(x, y, z) = xªi – 6j + yzk. div F= curl F=

A: To find  and  if .

Q: 2² 2! 2 x 24 4! 4 x + 26 6! 26 28 # + 8! %e = 1 - 2

A: 222!x2−244!x4+266!x6−288!x8+⋯=12,x∈[0,π]

Q: Find an antiderivative of 9x²–2x4 25 in the variable x where x = 0. Remember to include a "+ C" if…

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Q: For the given function f(x) and numbers L, c, and e> 0, find the largest open interval about c on…

A: Solution is given below.

Q: Use the fact that the derivative of the function gix)=√ is g'(x)=√ point x 100. The equation of the…

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Q: Start with the geometric series Σχ m=0

A: ∑n=1∞nxn,|x|&lt;1

Q: Use series to evaluate the limit. 1 - cos(2x) lim x → 0 1 + 2x - e²x

A: limit

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: The plane passes through points  and  and is perpendicular to the plane

Q: dv Draw a dependency diagram, and write a chain rule formula for dt Choose the correct dependency…

A: Given that To find:-

Q: A) Find the following integrals: 1) tan-¹(x) dx 1,5₂) 5. DYE

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Q: If cos(0) = sin(0) = and is in the 1st quadrant, find the exact value for sin(0).

A: given value

Q: a. Find T(t) and N(t) at the given point. x = e cost, y = e sint, z = e; t = 0 T(0)=

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Find the surface area of the portion of the cylinder x² + z² =4 above the rectangle R = {(x,y) |…

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Q: 3. (a) The region in Figure 8.35 is rotated around the y- axis. Using the strip shown, write an…

A: We have to write an integral for volume and evaluate it.

Q: Find a parametric representation for the surface. the part of the cylinder x² + z² = 49 that lies…

A: Given :Surface : Planes :  and Find the parametric representation for the surface.

Q: 8 S ( ² − 5 + £ ) da 6 dx X x² x³

A: I=∫(8x−5x2+6x3)dx

Q: Use a triple integral to find the volume of the solid that is enclosed between the paraboloids z =…

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Q: Fill in the blank with the correct choice. Suppose f(x) is decreasing over the interval [7, 13], and…

A: If a function f(x) decreases over an interval [a,b], which means..

Q: Estimate the volume of material in a cylindrical shell with length 46 in., radius 8 in., and shell…

A: Length 46 in., radius 8 in., and shell thickness 0.4 in

Q: Find Vw. W = xey sin 3z NOTE: Give your answer in unit vector notation; that is, in terms of i, j,…

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Q: Estimate the volume of material in a cylindrical shell with length 12 in., radius 9 in., and shell…

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Q: Find the distance between the points using the following methods. (-1, 5), (5, -3) (a) the Distance…

A: The given points are  and  the distance formula is given by:

Q: sin n (c)Σ, 0m2 + 1

A:

Q: Q3: A) Find (dy/dx) for: y² cosh(x+y)+ (tan(x)) sin(y) = eln(xy)

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Q: Uncover the 2 by 2 matrix such that: 61 6-2 [= =)= 10

A: Let

Q: A function f and its derivative f' are shown below. Assume a is a nonzero constant. Note: a is a…

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Q: The temperature of the air in Boise is given by the function f(t,h) = 0.01ht²0.12ht - 0.6ht² + 12t +…

A: Solution is given below.

Q: 1. Determine whether the statement is true or false. If it is true, explain why. If it is false,…

A: To determine whether each of the following statement is true or false.(a) If  is any constant…

Q: get the solving part but what I don't understand is how is goes from a number to sudenly becoming 0.…

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Q: Give a geometric description of the set of points in space whose coordinates satisfy the given pair…

A: Given that the set of the points in space whose coordinates satisfy the given pair of equations

Q: Find the derivative of y with respect to x. y = csc ¹(x²+1), X>0

A: Find the derivative of y with respect to x.y=csc−1⁡(x2+1),x&gt;0

Q: 1__dx x√x

A: