Find the equation of the tangent line to the curve y=5xcosx at point (pi,-5pi) the equation of this tangent line can be written in the form y=mx+b what is m? what is b?

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Q: Given that; f(2)=2, f'(2)-3 g(2)=6, g'(2)=4 Calculate the following (fg) 2= (f/g)'(2)= (g/f)'(2)=

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Q: (a) Explain how we can test whether the DE (cos y) dx + (y² - x sin y)dy = 0 has an integral…

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A: Given :A.3t+2y+3t+2yy'=0B.3t+2y+3y+2ty'=0

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A: Given data:- The given points is, A6, -2, 1B0, 5, 6C-3, -5, 2

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Q: The parametric equations of a cycloid generated by a circle of radius a is given by dy d²y x =…

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Q: Question Find the equation of the tangent line to the function f(x) = −3x³ - 2x² 33 x + 3 at the…

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Q: Rewrite csc 70 in terms of its cofunction cac 70°- (Type an exact answer Simplify your answer. Type…

A: topic- cofunction We are given , csc(79)°andcos2π7We know thatcsc(90-a)=sec(a)cos(90-a)=sin(a)

Q: Q.2 Find whether the following signal is odd function? f(x) = 5x³ 6(x4-4) even or

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Q: Solve the following initial-value problem: y'+ (tan x)y=cos²x; y(0) = -1 O y = (sin x) (cos.x - 1) –…

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Q: Question 4 Given: y'- y = xy5 and y(0)= 1, Find C OA.0 OB. 1/4 OC. 1/2 O D. 3/4

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Q: Consider the function f given by 2x f(x)=2x tan x if x ≤ 0, if x > 0, which is continuous at x = 0.…

A: The given function, fx=2x2-xif x≤0tan xif x>0 We have to check the function is continuous at x=0…

Q: Question & Determine which of the following tests would be best to use to determine the convergence…

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Q: Problem 2: Given the differential equation (yetanx sec² x - 1) dx + etanx dy = 0: a. Identify…

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Q: Given the differential equation (ysinx-cos²x) dx + cos x dy = 0 a. Determine if the differential…

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Q: Find the unique solution of the second-order initial value problem. y'' +18y = 0, y(0) = − 1, y'(0)…

A: The given differential equation is: y''+18y=0 So, we can also write as; D2+18y=0 The auxiliary…

Q: ouncements dules cussions des norlock Find the equation of the tangent line to the given function at…

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A: Find the derivative of cross product of vector r and its derivative.

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Q: Use the given graph of the function to find the x-values for which f is discontinuous. Answer…

A: The graph of a function is said to be discontinuous at a point where there is a break in its graph.

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A: Given query is to find the direction angles.

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Q: Determine the type of DE (select all that applies): 2xy dx + (y² + x²) dy=0 Linear Exact Separable…

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Q: Find the derivative of the function. f(x) = In(cosh(x)) f'(x) =

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Q: 12. Find the local maximuma, local minima, and saddle points for the function f(x, y) = x² + y² +…

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Q: If y = g(x) solves the initial value problem (IVP) Sy' = 4x + 12, y(0) = 20, and (x,y) is the…

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Q: Given the differential equation (xy + x + y + 1)dx + xdy = 0 that has a condition of y(ln2) = 0 b.…

A: given differential equation is solution below.

Q: :-√√3x lim x-3 27-x3

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Consider the DE x³y' + 8x²yy' + 4xy²y³ = 0. Making the substitution v = y/x in the DE yields 1 + 8v…

A: We need to write that the equation obtained after substitution is true or false.

Q: Find the solution of the differential equation r"(t) = (ellt-11,² – 1, 1) with the initial…

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Q: For the function defined below, find all values of x and y such that both fx (x,y) = 0 and fy (x,y)…

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Q: 7. Find the torque produced by a cyclist exerting a force of F = [70,30,160]N on the shaft- pedal a…

A: Given F = [70,30,160]N d= [12,15,11]cm

Q: Find the points on the surface x² - yz on the surface x² - yz = 5 that are closest to the origin.

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Q: If Q = 213030110 5 35 24 and Q-¹ - 91 93 92]. 94 what is the value of 92?

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Q: Differentiate the given function using the appropriate rule(s). Your answer does not have to be…

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Q: 4) Show that the surfaces 3X² + 2Y²+Z² = 9 and x² + y² + Z²-8X-6Y-8Z + 24 = 0 have a common tangent…

A: We have to prove both surfaces have common tangent at P(1,1,2).

Q: (x²y² + x² + y² + 1) dx + x² dy = 0

A: The given equation is  (x2y2+x2+y2+1)dx+x2dy=0

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Q: Let f(x) be given by the function, ƒ (x) = ln (x + ¹). x²-1 a. Show that f'(x) x³+x b. If g(x) =…

A: The given function is; f(x)=ln(x+1/x).

Q: 12 1.²³² 2. Consider a) Estimate this integral by using 4 rectangles with r 1 x+1 -da

A: a. right end points

Q: 4. The marginal profit from making and selling x products per day is P'(x) = 350 + 4x - 3x² Find the…

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Q: Given that; f(2)=2, f'(2)=3 g(2)=6, g'(2)=4 Calculate the following (fg)/2= (f/g)'(2)= (g/f) (2)=

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Q: Given: y2 + t2 + (e2y + 2ty)y' = 0, and y(1) = 0, Find: C (constant) O A. 1 OB. 0 O c. 1/2 OD. 1/4…

A: Given y2+t2+e2y+2tyy'=0 and y1=0