Find the curvature and the radius of curvature at the stated point. r(t) = 11 cos(t)i+ 9 sin(t)j + 2tk; t= 2 NOTE: Enter the exact, simplified answers. K. = ||

Q: Differentiate the following using logarithmic differentiation y = x=

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Q: Find (3+2)-2i. 406 754 386

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Q: The equation in slope-intercept form for a line passing through the point (- 3, 2) that is parallel…

A: Topic = Coordinate geometry Correct option = A

Q: (2, 4) y = 2x ng a vertical element of area, he area of the shased region is gven by the integral

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Q: no1

A: Topic:- application of derivatives

Q: The equation of the line passing through the point (– 3, 7) with slope zero. A. x = -3 C. x = 7 D. y…

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Q: Find V. (V x F) if F(x, y, z) = 4 sin xi + 5 cos(9x – 10y)j+ 10zk. V·(V × F) =

A: topic- vector field

Q: Solve for the differential equation: dy/dx - ytan x = cos x

A: To find the solution of the linear differential equation of first order y'+Py=Q, where P and Q are…

Q: =

A: We will find the derivative.

Q: The force F (in newtons) of a hydraulic cylinder in a press is proportional to the square of sec x…

A:

Q: Determine whether the series converges absolutely or conditionally, or diverges. (-1)" n + 2 n = 0…

A: Alternating series test:∑n=0∞ (-1)nn+2an=(-1)nn+2bn=1n+2limn→∞1n+2 =0and bn+1-bn=1n+3-1n+2…

Q: If f is just that = e*[- sin(x + y) + cos(x +y)] and -e sin(x+y) which if the %3D ay following is…

A: On solving this we will get:- Option (A) is correct.

Q: Show that the function f defined by 1. (x, y) = (1, –1) f (x, y) : x² + y .2 (x, y) + (1, –1) x + Y…

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Q: Consider F and C below. F(x, y, z) = (y²z + 2xz2)i + 2xyzj + (xy² + 2x²z) k, C: x = Vt, y =t + 8, z…

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Q: e3t – 1 lim t0

A: Use l hospital rule for finding the limit.

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A: we are given the function f(x)=cos(x) and the interval -π3,π3.The function f(x) is continous on the…

Q: The arc y = x² from (0,0) to (2, 4) is rotated about the y-axis. Find the area of the resulting…

A: We want to find surface area

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: Find the limit. 421 (a) lim 7+ 17 (b) lim x-0 X 3

A: Topic = Limits

Q: 1. S 2xe2*dx

A: Given that,   Using integration by part

Q: Explain why the integral is improper. 18 .6 1.4 1.2 y F0.8 F0.6 F0.4 F0.2 -2 -1.5 -1 -0.5 At least…

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 00).…

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Q: EXAMPLE 1: Consider the graph of the funetion f given below. Using the given graph, determine if the…

A: topic- continuity of a function

Q: 1 Σ 6" - 5 n = 1 8

A: Given :

Q: .5 2. 2. dx =D dx- (6+z*) o o (x²+9)½ 's (x²+9)½

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Q: (А) True B) False

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Q: Step 3 Apply the Fundamental Theorem of Calculus, which states that f(x) dx = F(b) - Fa). Use this…

A: We can complete step 4 by the cross multiplication method.

Q: 4) Find all values in the interval [-27,27]at which the graph of f has a horizontal tangent line.…

A: topic- functions and derivatives

Q: Csin $ 3 y cos*3 ychy

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Q: 3 In ДАВС, с % 15 ст, b — 4.6 ст, тLA: = 106°. Find the area of the triangle and round to the…

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Q: Use the definition of Taylor series to find the first three nonzero terms of the Taylor series…

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Q: Consider the following. h(x) = ex2 − 4   Find  h '(x)=   Solve  h '(x) = 0 for x. x=   Find  h(0)=…

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Q: pind tue indefinete integral S In(s-1) ds

A: ∫ slns-1dsLet u=s-1=∫u+1lnudu=lnuu22+u-∫12u+2du=lnuu22+u-u24+uSubstitute back…

Q: Evaluate the defınite integral. i+e"j+t k)dt O el2 12-( - 1) + O el2 – 1 i+ (e-' – 1) j + k el2 – 1…

A: ∫01e12ti + e-t j + t kdt=e12t12i -e-t j + t22 k01=e12112i -e-1 j + 122 k-e12012i -e-0 j + 022…

Q: 26 State the Fundamental Theorem of Calculus . you must state the first and the second fundamental…

A: On solving this we will get

Q: FInd Fas a function of x and evaluate it at x = 0, x = 7T/3, and x = /2. FX) = F(x Cos 8 de Fx) FO)

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Q: d) Use the right endpoint rule to approximate the area under the curve of f(x) = 4- x2 on [1,2]…

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Q: Which of the following differential equation has the same order and degree? [dy]6 + 5y = e* A. + 8…

A: See the answer below

Q: Evaluate this double integral. Avoid integration by parts. Hint: Can you reverse the order of…

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Q: 7.372 The rate of change of the weight of a mouse, can be modeled by r(t) grams per week, where t t…

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Q: Finding the work done in lifting a leaking bag of cement. A bag of cement originally weighing 143 lb…

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Q: Find the direction angle of v for the following Vel v = - 6i- 3j What is the direction angle of v?

A: On solving this we will get

Q: Evaluate the limit using L'Hospital's rule 4* – 97 lim

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Q: Let f(x) = - 5 sec(6x) f (x) =

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Q: 2. Use the limit theorems to find the following limit. x2 – 5x – 14 lim x→7 x - 7

A: Given :limx→7x2-5x-14x-7

Q: Evaluate the limit V5 + 7x² lim 5 + 4x I+ 00

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Q: Find the area between the curves f(x) = x2+2x+1 and g(x) = x+1

A: We need to find area between given curves.

Q: Solve the following differential equations: d³y dy d?y 3- + 3 dx2 В. dx3 dxy=4e*

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Q: Calculus The sales in thousands of a new type of product are given by S(t)= 260-90e-0.2t, where t…

A: Topic:- application of derivatives

Q: Find 17. d Ssin (4x) cos(4x) dx

A: Use substitution to solve