Evaluate Limit= Hint: Use the power series expansion of cos(x). lim cos(x) − 1 + ²/ 14x4

Q: 7. Using differential, approximate (8.01 ) correct to 4 decimal places. 8. Use differential to…

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Q: 1 find the total differential dz. axeta TU

A: Find dz

Q: Describe the graph of the equation. r = 3 sin 16t i - 3 cos 16t j O It is an ellipse in the…

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Q: Find T(t) and N(t) at the given point. (7) = N() = = T r(t) = 11 cos(t)i + 11 sin(t)j + tk; t = K|2

A: Given,…

Q: Find the value(s) of c such that n=0 enc = 10

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Q: d Calculate =[rı(t) · r₂(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly…

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Q: -2x Find the derivative of f(x) = xe O f'(x)=e-2 (e-22) ²- O f'(x)=x²e-2 (²-2) O (E) None of these O…

A: We have to find the derivative of  f(x) = xe-2x.

Q: 16. Let u = ln t, t = 2r and r = √w. Find and simplify du dw in terms of w.

A: As per Bartleby guideline,  we have answered only the first question. Please repost mentioning the…

Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A: Given problem:- Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to…

Q: 01) Solve the differential equation with the given initial condition: y' - 6x²y + 4xy = y. where…

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Q: 12. Prove that the intersection of any family of normal subgroups of a group (G, *) is again normal…

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Q: x = 10t, y = t², (0 ≤ t ≤ 1). In each part, evaluate the line integral along C. NOTE: Enter the…

A: To find the values of given line integrals.

Q: Find the maximum area of an isosceles triangle inscribed inside the ellipse x²y² 1, + = a² 62 with…

A: Given problem:- Find the maximum area of an isosceles triangle inscribed inside the ellipse x2/a2…

Q: Homework 12 Polar: Problem 2 The limacon r = 1+ csin(0) has an inner loop when |c| > 1. (a) When c>…

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Q: 8. SHOW ALL WORK =I Determine the values of the other five trigonometric functions of 8, given that…

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Q: Determine whether the following Consistent or not a) 5x +2y = 1 3x +2y = 1 b) X₁ + X₂-2X3 + X4 = 9…

A: Here, to check whether the given system is consistent or not.

Q: d Calculate[ri(t) r₂(t)] and[ri(t) x r₂(t)] first by differentiating dt the product directly and…

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Q: = [₁²2² I = x² dx I = fa da x

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Q: Find the exact length of the curve. X √(y - 3), 16 ≤ y ≤ 25

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Q: Evaluate the integral 13 ƒ(x)dx geometrically for ƒ (x) = { |3 − x ; x ≤ 5 2; x > 5

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Q: x² 5x w Given that f(x) 3 a) find f'(x) b) find the equation of the tangent line x = 1. 1 12. Given…

A: Let's find.

Q: Finding an Indefinite Integral In Exercises 75-78, find the indefinite integral. 1 75. dx 7x-2

A: Here is the solution:

Q: 12. SHOW ALL WORK Solve the equation for all t in the interval [0°, 360°). Express answers in…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: A 10,000 litre rainwater tank is to be built in the shape of a cylinder. It must be at most 3 metres…

A: As per our guidelines we can answer only 3 subparts of the given equation. Kindly repost the…

Q: Find the indefinite integral. (Use c for the constant of integration.) [(48³1 + (4t³i + 14tj -…

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Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² − c² and y = c² – x² is…

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: If a rock is thrown upward on Mars with velocity 10 m/s, its height (in meters) after t seconds is…

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Q: The differential equation regarding the family of curve y = e 500x 1S

A: This question is based on diffrential equation.

Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: Evaluate the definite integral. 15t L² (elst i + e i+e¹j+t k dt 1 k)di

A: Here we have to use the concept of definite integral.

Q: Particle Motion In Exercises 49 and 50, the velocity function, in feet per second, is given for a…

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Q: Homework 11 Parametric: Problem 2 Eliminate the parameter t to find a Cartesian equation for: and…

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Q: Find the limit. lim (t i 6 j + t² k) t-5 lim (t i − 6 j + t² k) = i t-5 i+ i j+ i k

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Q: y" + 6y' +5y=10sin (2x)

A: First find AE(Auxiliary equation) and PI ( Particular integral)  then CS ( Complete Solution) is PI…

Q: Consider the curve C of equation: (x² + 2y + y²)² = 4(x² + y²). From the following options choose…

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Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x)…

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Q: Using the Mean Value Theorem In Exercises 13-18, determine whether the Mean Value Theorem can be…

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Q: alyze and sketch a graph of the function. Label any intercepts, relative extrema, y = x² - 8x + 37…

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Q: f(x) = 2x + 3 x 1 1 ; a = 1

A: limx→1+f(x)=limx→1+x2+2                =12+2=3limx→1+f(x)=3

Q: Solve the following initial value problem: y′′+6y′+18y=0y″+6y′+18y=0 when y(0) is 5 and y’(0) is…

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Q: Applying the First Derivative Test In Exercises 29-36, (a) find the critical numbers of the function…

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Q: Solve the following differential equations of y"-2y' +24y=3sin(4x)+6cos (7x)

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Q: = ||r' (t) x r' (t)|| ||r' (t)||³ to find k(t). r(t) = 7 cos(9t)i + 7 sin(9t)j + tk Use the formula…

A: find curvature

Q: Find the derivative for each function. ㄷ 7. y=x² +2 9. y=2x²-x+3 A. 6. y=3x²-6 8. y=x²-3x+2 10.…

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Q: Check the function y=x²+1 whether have a symmetry about x or y axis

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Q: we have 27ft squared of material to build a box of maximum volume with a square base and no top.…

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Q: Solve for the solution of: (D2 - 4)y = 8e2x - 12

A: Given problem:- Solve for the solution of: (D2 - 4)y = 8e2x - 12

Q: Find a vector parametrization of the ellipse centered at the origin in the xy-plane that has major…

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