Use Theorem 13.9 to find the directional derivative of the function at P in the direction of  PQ. f(x, y) = e5y sin(x),    P(0, 0),    Q(2, 1)

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Q: tan3 -dx sec x

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1)

A: To find the gradient of the function at the given point.

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x2 - y2, (7, 4, 33)…

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Q: 19. (+ 2x 4) dx

A: ∫ af(x)±bg(x) dx = a∫f(x) dx ± b∫g(x) dx . ∫xn dx = xn+1n+1+C

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Q: Which of the following is a solution of the equation 11 · 4* = 7 · 5*? Select one: a. x = 11/7 b. x…

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Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

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Q: Diagonalize the following matrix. One eigenvalue is i = 4 and one eigenvector is (-6,3.2). - 14 - 36…

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Q: Evaluate (x² + In(y) +z )dV B = {(x, y, 2) | 0 <I< 1,1< y < 7,0 < z < 6} . Round your answer to two…

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Q: 1.) xy2dx + y³secx dy = 0 %3D 2.) (5- t)dx- (2x + 3)dt = 0 3.) 4dy + y dx = x² dy

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Q: dy 6-x.-3y= x' dx

A: we are given an ode -x*dy/dx -3y=x2 we have to solve this ode as we can see, this is a linear first…

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A: The given integral,       ∫1∞3-2x-32dx

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

Q: Let a = ci + jand b = 3i + 4j. Find c so that the angle between a and b is- Round your answers to…

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Q: c. f(x) = (-1 if x 0 %3D

A: We need to find possible points of discontinuity.

Q: 2. g'-yso ylo)=2 gilo): -2 y'Co)= y'(0)= -2 : -2

A: Given: y''-y=0, y0=2, y'0=-2 So, we can also write as: D2-1y=0   The auxiliary equation is: m2-1=0

Q: Consider the differential equation y' + y² = t*e*. Which of the terms in the differential equation…

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Q: Find an equation of the plane through (-8, –4, –5) that is 2 = t, y + 3 | perpendicular to the line…

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Q: Answer(7) Linear First Order D.E. Solve the following differential equations of 1-e" dx +2(xe" –…

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Q: 33. (1 + r)' dr

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: 1 The series > is convergent. (Зп + 1)(3п + 4) n=1

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Q: | cos(V) dx 2 Vx sin (Vx)-2 cos (Vx)+C C 2 Vx sin x (Vx)-2 cos (Vx) + C 2 Vx sin (Vx) + 2 cos (Vx) +…

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Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(1,…

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Q: 9. cos(x-)

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Q: A curve C is defined by the parametric equations x = 1– t2 y = t – t3 (a) Show that C has two…

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Q: Consider the Bernoulli's equation: dy - y = 6e*y³. dx A) Find an appropriate substitution and reduce…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Consider the following IVP: Find the general solution. 1. y"-3y'+2y = e3t ; y(0) = 0, y'(0) = 0

A: According to our guidelines, we can answer only one question. Other questions can be reposted.

Q: Calculate the following sums. (Use symbolic notation and fractions where needed.) 8. (a) i=1 8 (b)…

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Q: Given the parametric function fill in the table. x (t) = t3 - 2t %3D y (t) = t - 3 t x -2 -1 1 2.

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Q: 3. Evaluate the following using Integration by Parts, Algebraic Substitution, Trigonometric…

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Q: Find the directional derivative of f(x, y, z) : 4y at P(3,1, –2) x + z in the direction from P to…

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Q: 8.) y Inxlny dx + dy = 0

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

Q: If f(x) = 2x - 1, what is the equation of the normal line to the graph of fat (1, 1) O A. x - 6y = -…

A: 1) f(x)=2x3-1 at (1,1) 2)f(x)=g(u) and g(u)=u(x).

Q: Your explanation should answer WHY you are doing the work and HOW you are doing the work briefly…

A: If f'x is:→ then fx is-ve→decreasing0→horizontal +ve→increasing=a &amp; ≠0 →slant with slope…

Q: 10. * S sin(In x)dx 1 C x sin(Inx) – cos(Inx) + C 2. x sin(Inx) – cos(lnx) + C 1 x sin(lnx) +…

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Q: Find the relative maximam/minimum values of the fuction てキX Stak where the Function S increasing of…

A: For a given function, y = F(x), if the value of y is increasing on increasing the value of x, then…

Q: Which graph closest models the following parametric equation on the domain -2 < t < 2? x (t) = t3 –…

A: Given that       x(t) = t3 - 2t      y(t) = t2 - 3

Q: 22. Which of the following statements about the functions y = f(x) and y f(x) is true? A. If the…

A: Here, to find the correct statement for the functions y=f(x),y=1f(x)

Q: (cos x+xcost)dt +(sint – t sin x)dx = 0 Ans. t cos x+x sint = c

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Q: C Solve the following problems. 16. What value of k makes the function continuous at x= 3? Graph the…

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Q: In V3 dx 1+e2cx

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Q: Determine whether the lines L1 and L2 are parallel. L: x = 2 – 31, y = 4 +1, z = 7- t L2: x = 5 –…

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Q: Evaluate e |/| 2xz dV where E = {(x, y, z) | 0 < z < 1, ¤ < y < 2x, 0 < z < z + 3y} E Round your…

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