Find the arclength of the curve r(t) = (10√√2t, e10t, e-10t), 0≤ t ≤<1

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Q: 1. Prove using index notation. ABC REF = AB (c@f) E¹: R ":"product is defined as where := Pij Qiz…

A: Given ......  A~B~c~ · D~E~f~ = A~B~(c~⊗f~)E~T:D~                 Where,…

Q: Then Graph, emphasize the Limit. 5. lim x-3 √²-5+2 x-3

A: limx→3x2-5+2x-3 We have to find the limit.

Q: If 6x²y + xy² = 7x, find y' by implicit differentiation. y' =

A: Solution is done in step 2

Q: Suppose that lim f(x) = 9 and lim g(x) = -5. Find the following limits. X-4 X-4 a. lim [f(x)g(x)]…

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: Find da f 2log 2 In z O None of these O 20, 2 In 2 O2: In 2 O2 In 2 +C +C +C

A: Integration problem

Q: 11 8 xr xeza S. XE 16.

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Q: 2 3. Find a number b such that the limit d. The picture shoolim h→0 exists, then find the limit.…

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Q: Find the derivative of the following inverse trigonometric functions. 3. y = xarcsinx + √1-x²

A: Given:      y=xarcsinx+1-x2 differentiating on both sides    dydx=ddxxarcsinx+1-x2…

Q: Let f(xy) = x²-3x

A: Concept: Partial derivative with respect to x fxuv=v∂u∂x-u∂v∂xv2

Q: For f(x) = 3 x+3 and g(x)= find a. (fog)(x) b. the domain of fog

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Q: Use implicit differentiation to find an equation of the tangent line to the curve -4x² + 1xy - 3y³ =…

A: This question can be solved using the concept of tangent and normals.

Q: the answer is wrong

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Q: go O II 6 Paragraph For f(x)= x2+4 and g(x)=x2-4 find the following function (gof)(2) HE 7 Ty F8 G…

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Q: Find the directional derivative of g (a, b) = cos(3a + 4b) at the π point ( along the direction of…

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Q: By cutting away an x-by-x square from each corner of a rectangular piece of cardboard and folding up…

A: Since, it is given that by cutting away an x-by-x square from each cornerof a rectangular piece of…

Q: dy dx + 2y = f(x), y(0) = 0, where f(x) = 1, 0≤x≤

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Q: Find the initial value a, growth/decay factor b, and growth/decay rater for the following…

A: We have given  Qt=0.00292.52-4t Qt=0.002912.544t Qt=0.0029(0.024025096)t Comparing We with equation…

Q: In R TOHE R² 1 √√3 J₁ 1 dR arctan(1/x)dx

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Q: Find the particular solution: dy siny = dx cosy(1-xcosy) when x=0 and y=0

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Q: The graph of f(x) is shown below. Which of the following statements are true? 8 7 60 5 4 3 2 1 M -8…

A: Ax x=6, limx→6-f(x)=limx→6+f(x)=f(6)

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A: Need to find out the intervals on which the function is increasing, decreasing and also the value of…

Q: Find the general solution of the differential equation Write your solution in the form F(x, y) = C,…

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Q: 1. Solve the following equations: - a) b) c) log₂ (5x - 1) - log₂ (16-3x) = 5 253x+2x625 1258x = 1…

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Q: 1. lim 1-3 √x+1-2 x²-9

A: Topic:- calculus

Q: Find r(t) u(t). . r(t) = (5t4)i ³j+2k u(t)= t²i4j+t³k r(t)u(t)= Is the result a vector-valued…

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Q: velocity speed f(t) = 85t - 5t² I m/s m/s

A: Given; f(t)=85t-5t2, t=3.

Q: For f(x) = 10/x and g(x) = 10/x, find the following function (fog)(x) U I=

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Q: SOLVE THIS: II. Find the relative extrema and saddle points of the following function. x3 f(x, y) =…

A: extreme points of function  fx, y=3x+xy-y2-x33

Q: If f(x) = 5x√√x+2 what is the value of (f-¹)(20)? Select one: 4 O a. O b. O c. | | 25 Check 25 O d.…

A: If fx=5xx+2, then to determine the value of f-1'20.

Q: 3x² - y2 + 18x-2y-10=0 4x²-4y²-8x-8y-19 = 0

A: Given Equations:- 1. 3x2-y2+18x-2y-10=0 2. 4x2-4y2-8x-8y-19=0

Q: Find Əx Select one: O a. O b. if Sxy= 3x +y10 O C 3-8y 10y⁹ - 8x 8x-3 10x 8y-9x 10

A: The given equation is; 8xy=3x+y10.

Q: Transform the following equation of ellipse in standard form. 4x²-4y²-8x-8y-19 = 0

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Q: Use trigonometric substitutions to evaluate the definite integral 1 [5x²³√1-x² dx.

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Q: The graph of f(x) is shown below. Which of the following statements are true? 00 7 6 5 4 3 2+ H -5 Y…

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Q: S dx 2 (1+x²)²

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Q: y = f(x) N.K. X -1- (a) lim [f(x) + g(x)] (b) lim [f(x) = g(x)] - (c) lim [f(x)g(x)] -1 y 1 y = g(x)

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Q: If x¹ + x²y + 7y² = 14, find y' by implicit differentiation. 2

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Q: Question 8 v Find the derivative of: - 4x + 6x⁹

A: Given question:- Find the derivative of   -4x8+6x9 Topic :- derivative

Q: Find a and b such that f is differentiable everywhere. 2 cos (r) if r 0 a = b= f(x) = {

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Q: Let v = (7,8). Suppose w E R² is perpendicular to v, and that ||w|| = 7. Find both possible vectors…

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Q: Consider the following. 1 - 2x² x42x² + 3 Let u(x) = 1 - 2x² and v(x) = x² − 2x² + 3. Find each…

A: We need to find derivative.

Q: y = x ln(x + √1 + x² ) − (√1 + x²

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Q: Assume that a body cools according to the Newton's Law of cooling. Find the temperature (T) at time…

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Q: J. 1-76 Fomts] + (a) For the function g whose graph is given, state the value of each quantity, if…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 14…

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

Q: Q2. Using cylindrical coordinates to find the volume of the region bounded below by the cone z =…

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Q: Solve the given DE using the appropriate method. Show your COMPLETE solution. (D³ – 6D² + 12D – 8) y…

A: Given :D3-6D2+12D-8y=0