Prove that the radius of curvature of the Helix curve (helical spring) r(t) = (cost,sin t, t) is constant.

Q: the answer on my test corrections is showing 2 with margin:0, could you explain more?

A: To evaluate the following limit. limx→0 sin6xx2+3x

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Q: 1. Consider the function ax² + bx - 3b ax + 15 Find the values of a and b such that this function is…

A: Given function:- fx=ax2+bx-3bif x<2ax+15if x≥2

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Q: Sentwork Solve y'" - y" = e³x + 3e4x y = C₁ + C₂ x + C3e* + 18 e 3x + 16 4x

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Q: Find an equation of the tangent line to the given curve at the specified point. 1 + x 6 + ex' (0,…

A: Given: y=1+x6+ex, 0, 17

Q: n(# ) dx + y (lny³ + ln x³) dy = x² sin is a homogeneous equation.

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Q: 2 yt Jy - 25 - 2 dx

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Q: Find the distance from the point (1, 3, -4) to the plane x − 3y + 3z = 9.

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Q: f g(s,t)=10s*e3st-7t^2 gs(s,t)=

A: Given g(s,t)=10se3st-7t2

Q: Seatwork For ye Step y" ~ly = 0 m² -1=0 (m+1)(m-1)=0 m= 1₁ -1 Solve y" - y = 3e* f(x) = 0 Casel Yc =…

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Q: Over a 24-hour period 0 ≤ t ≤ 24, the power drawn by a household is given by the function p(t) =…

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Q: dx Evaluate the integral 2x log x 7X

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Q: An general equation for the plane passing through the points (-5, 4, 4), (–6, 4, 3), and (-7,1,5) is…

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Q: 1/n n=19+(Inn)² 15) Σ. test: converges/diverges

A: Given seires:- ∑n=1∞1n9+lnn2

Q: Evaluate the integral. 3 L²F(x) -4 f(x) dx where f(x) = (3 16- x² if -4 ≤ x ≤0 if 0 < x≤ 3

A: Given function:- fx=3if -4≤x≤06-x2if 0&lt;x≤3

Q: Find the intervals where the following functions are increasing: (In x)24 (b) y = ln (e +e=x) (c) y…

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Q: What is the probability that a number selected at random from the first 1,000 positive integers is…

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Q: 37. dx dt dy dt dx dy +2 dt dt = 2x + 2y + 1 || y + 3

A: To solve differential equation.

Q: Questions 12-15: Determine if each series converges or diverges. Indicate which test you are using…

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Q: At time t the position x(t) = 10 sin(t) is given by the following. *() - 10 sin() =10 එය = 3 15√3 T…

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Q: Differentiate y = sin 4r. y

A: Derivative

Q: 6. T 0 sin x √cos x dx

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Q: Sketch the region of integration and change the order of integration. rIn(x) 1 J0 f(x, y) dy dx f(x,…

A: We need to sketch the region and change order of integration.

Q: x*cosh x³-2 dx

A: given integration is I = ∫x4 cos hx5-2 dxthen we have to evaluate it

Q: Find the slope at the point (1, 1)  for the curve defined implicitly by ln y = x2 – y2.    a m = 2…

A: Given query is to find the slope of the function.

Q: Find the tangent plane to the equation z = 4y cos(5x – 3y) at the point (3,5,20) z =

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Q: f(x) = 2x^2/2x^2-1 Find x- and y- intercepts Find all vertical asymptotes and horizontal…

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Q: Find y' and y". y = cos(x²) y' -sin(x²).2x ✓ = y" =

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Q: 55. z = у 2х + 3у

A: As per Bartleby guidelines only one question is allowed to solve so i will solve 55 for you if you…

Q: [6-S] [CLO 8] Show, in a mathematically rigorous way, that if (x₁, y₁) and (x2, y2) are two (not…

A: We will find the required.

Q: x^2y"-5x'+9y=0  y'(0)=y(0)=0 Solve this DE

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Q: Evaluating and Solving Radical Functions A person's Body Mass Index is calculated with the formula:…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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Q: Date Note Evaluate S √9-x² dx (use Trigonometric substitutions)

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Q: Solve for the general solution of the equation: y" +4y=-x+4e², Ⓒy=c,cos2x+c sin2x -0.8x+0.25e…

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Q: For the function f(x) = x³ + ax² + 2a²x + a, there exists a point of inflection at x = 2. Determine…

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Q: Suppose f(x) = 7x²+5x. Find: ƒ'(1) =

A: Given: f(x) = 7x2+5x

Q: An arithmetic series is defined by the formula a = 6n-3. a) What is the first term of the series? R…

A: Given query is to find nth term and the sum n term .

Q: A 5 foot ladder is leaning against a wall. If the foot of the ladder is sliding away from the wall…

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Q: ! A N AR 2 W S 199 Let à =(-4,-5, 3) and 6 = (-5, 2, 4). Find the projection of b onto a. proj 6=<…

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Q: The region R is bounded by the x-axis and the graphs of 3 2 = 2. A part of R. is shown as the shaded…

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Q: Determine if = 5₁° f(x) dx is convergent or divergent when G 1 x² and find its value if convergent.…

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Q: Find the distance from the point (-1,9, 3) to the line ä(t) = (2,-2,-4)t + (-6, 6, -1). I ines Tai

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Q: Express the integrand as a sum of partial fractions and then evaluate the integral. Express the…

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Q: escribe how the graph of y = log1/ -4 relates to the graph of y = log(x).

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Q: f(x) = (-8x²9)³(-9x²-4)-12

A: we will find the required.

Q: Let f(x,y) = 3x^y + 4xy³. Find 224 224 224 224 2' ахду' дудх and ду 2' ах

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Q: 6. Find the area of the region in the first quadrant which is bounded by y = 3x -8 and y=4-x a) 20/3…

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