Find the curvature and the radius of curvature at the stated point. r(t) = 4 cos(t)i+5 sin(t)j+ 6tk; t= 2 NOTE: Enter the exact, simplified answers.

Q: For the rational function f(x) = find the following limits and identify the type of asymptote that…

A: Given: Rational function: f(x)=4x-1x+9

Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

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Q: Evaluate the definite integral. (Round your answer to two decimal places.) 1 9 (cosh(x))² dx

A: cos h(2x)=cos h2x +sin h2xcos h(2x)=2cos h2x -1cos h(2x)=1+2sin h2xcos h2x =1+ cos h (2x)2

Q: g=ズ, a find dy dx %3D

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Q: Find f and f, and evaluate each at the given point. 3xy f(x, y) = V2x + 2y (1, 1) " (x, y) = 5,(x,…

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Q: Express the limit lim E (4 cos (272;) + 6)A¤; [2, 4] over as an integral. n- 00 i=1

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Q: When the eigenvalues of a b A = 0 d are 2, = 0 and 2, = 2, what are the possible values of a and d?…

A: When the eigen values of A=ab0dare λ1=0, and λ2=2, then to determine the possible values of a and d.…

Q: f (x) = x² + 1

A: Given :

Q: Describe the graph of the equation. r = 12 sin 6t i – 12 cos 6t j O Itis a circle of radius 6 in the…

A: To find: Discribe the graph of the equation

Q: Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. f(x) = cot x, a = - Po(x)…

A: As we know that; The Taylor series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+… Where centered at x=a.…

Q: 3. f(x) = 8

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

Q: Use the derivative formula below to compute the derivative of f(x) = x2 - 5x. SHOW WORK. You may…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

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Q: For what values of S is the solution space of the system given below the origin only, a line through…

A: In the given question we have to find the values of s for which the solution space passes from the…

Q: If 39 | f(z)dz = 7 - 89 and - 39 g(x)dx = 25 89 and 39 | h(x)dæ = 32 89 what does the following…

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Q: EXAMPLE 6 Evaluate the following integral. tan (r) dr SOLUTION First we write tangent in terms of…

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Q: Consider a triangle ABC like the one below. Suppose that b= 33, a=48, and B 26°. (The figure is not…

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Q: Find div F and curl F if F(x, y, z) = 13y'2*i – 11x°z®j – 7xy°k. %3D div F= 0 curl F=|(-35 z y³ + 99…

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Q: Question 1 Give an integer a E Z which makes the following equality true for y = x". 7 log.ry (y) 8…

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Q: Determine the vector field of F. F(x, y) = yi - xj

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Q: Solve the higher order initial-value problem f''(x) = x-1/x + 3 ; f'(1) = 3, f(1) = 0

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Q: (x) = V19+r dt , find f'(3)

A: Given query is to find indicated derivative.

Q: Find V x (V x F) if F(x, y, z) = 6xyj+2xyz k. V × (V × F)

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Q: Evaluate the following definite integrals. dr 5. ? +3

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Q: Evaluate the integral by making the given substitution. (5x)tan(5x)dx, u = 5x + C

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Q: メーャゴ+2x)dメ+でyalyo

A: answer is in next step .please give a like

Q: Verity Gauss' theorem for the vector feld f (x,y, z)= (y,x,2) on the surface of the sechere with…

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Q: Find the particular solution determined by the given condition. F(x) = 3x2 - 2x; f(O) = 9 %3D %3D O…

A: Given query is to find the solution of the differential equation.

Q: (2.x+ 5y)dx + (4.x – 5y)dy =

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Q: Use partial fractions to evaluate the definite integral. Use a graphing utility to verify your…

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Q: the in integra a) (x³ + 1)dx

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

Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: What u-substitution should be made in order to evaluate the following integral? dx (6x² + 4)* u =

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Q: If f(x) cos-(2x+5) 2, then dom(f) = %3D a+3 (A) (–3, –2) (B) [-3, –2] (С) (-3, —2] (D) (–1,1) (E)…

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Q: 4. Consider the figure below. y=4 x Find the volume of the solid generated when the shaded area a.…

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Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

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Q: dx (r-1)%

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Q: Use Newton's method with the specified initial approximation x, to find x3, the third approximation…

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Q: dx (х -1)3

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Q: The point P(4, 24) lies on the curve y = z + x +4. If Q is the point (x, x² + x + 4), find the slope…

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Q: / (3V-1)dt is 3- 1 by the 2nd fundamental theorem of Calculus. The derivative with respect to x of 3…

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Q: Evaluate the integral (12x + 6y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Find the equation of the tangent line to the curve g(x) = 5x2 - 6x +2 at the point (1, 1).

A: Use equation of  tangent line

Q: Consider a surface defined by F(, y, z) = 0 whose gradient is (cos(Tx), z? e", 2ze"). The equation…

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Q: Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is…

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Q: 7. Find the area of the region bounded by y = 5x² +1, x = 0, x = 2,y = 0. Give a sketch of the…

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Q: 2. A force of 5.0N is applied at the end of a lever that has a length of 2.0meters. If the force is…

A: We need to find the torque when we are given values of force  & length of liver and angle to the…

Q: The graph of the function f(x) = sin(x+ 8) is shown along with the points (– 8, f( – 8)) and (– 7,…

A: (1) f(x)=sin(x+8)f'(x)=cos(x+8)slope =f'(-8)=cos(0)=1equation of tangent at…

Q: plapii the function f(t) = 6t(h(t – 1) – h(t – 6)) for 0<t<o. Use your graph to write this function…

A: Heavyside function

Q: Given a function f(x, y) = In(9 – x² – y²). (a) Find and sketch the domain of the function. (b) Find…

A: Given function f(x,y)=ln(9-x2-y2 )