||r'(t) × x r" (t)|| Use the formula k(t) to find k(t). r(t) = t’i + tl5j %3D K(t) :

Q: Find the domain of r(t) and the value of r(to). NOTE: Roumd your answer to two decimal places when…

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Q: a. Find the linear approximating polynomial for the following function centered at the given point…

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Q: h. Average value of f on [-4,-1]

A: From graph  f(-4)=5f(-1)=7   formula for average value

Q: For the given p-series, identify p and determine whether the series converges. Σk-9/8 A=1 P =…

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Q: The traffic flow rate past a certain point on a highway is q(t) = 1300 + 2200t – 390,² where t is in…

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Q: Find the arc length L of the graph of r(t). r(t) = 12 cos(t)i+ 12 sin(t)j + tk, 0<t< 2n L= 75.66

A: arc length

Q: 5. Evaluate [62³e¹dA; R= [0, 2] × [0, 2] R

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Q: 1. √x √1 + x² dx X

A: Solution:

Q: Determine the exact area between the x-axis and the curve defined parametrically by 2 x(t) = - +² t²…

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Q: The curve is given in polar coordinates by r = e³0. Let A be the point on the curve corresponding to…

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Q: The equation of motion of a particle is s = t4 - 3t3 + t2 – t, where s is in meters and t is in…

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Q: √x²√9 - x² dx

A: We will solve the integration,

Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and…

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Q: 3. [_x dx √2 +*

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Q: Evaluate the product for the following using a sum or difference of two functions. cos(45°)…

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Q: Find an equation for the tangent line to the curve parametrized by x = 4t y = est at the point t =…

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Q: リ= 3x3-x2+6

A: Given query is to find the equation of the tangent.

Q: An object moving along a horizontal coordinate line has directed distance s(t) = t - 6t2 + 9t + 11…

A: s(t)=t3-6t2+9t+11 Differentiating with respect to t s'(t)=ddt(t3-6t2+9t+11)=3t2-6*2t+9+0=3t2-12t+9…

Q: 3. Find an equation of the tangent plane at P = (0, 3, –1) to the surface with equation ze" + elz+1)…

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Q: Sketch the vector field F(x, y) = xj, the line segment from (6, 1) to (6,5), and the line segment…

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Q: Suppose f(5) - 9 and f'(5) = = - 3. - An object moves along the curve y³ - 3x² f(x) = 5x = 649. For…

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Q: 2. Given the function f(x) = 2x² + 3x + 1, a. Use the secant method to find the instantaneous rate…

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Q: Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and…

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Q: Consider the following. y = √x 4 X = 8 y = 2-x -6 -8 (a) Form the integral that represents the area…

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Q: Determine the behavior of the functions defined below. If a limit does not exist or the function is…

A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost…

Q: Consider the following theorem. Theorem If f is integrable on [a, b], then [ºf(x) dx = dx = lim…

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Q: 4. S (x + 1) √2x − 1 dx

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Q: Write the integral in terms of u and du. Then evaluate. u = 812 + 1 (Use symbolic notation and…

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Q: 11. If f"(x)=-4sin 2x, f(0)=0and f'(0) =2, find the value of f 4

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Q: Find the slope of the tangent line to the curve x² - xy - 2y³ 116 at the point (-2, 4).

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Q: Consider the curve parameterized by x = 3t²3 and y = 2t³. Find equations for all tangent lines to…

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Q: The volume of a right circular cone of radius a and height y is given by V = dy volume of the cone…

A: Explained below

Q: a. Find the slant asymptote of the graph of the rational function. b. Follow the seven-step strategy…

A: We need to find slant asymptote.

Q: (−1)n! What is the Find the Taylor series for f centered at 4 if f¹" (4): 3″(n+1)* radius of…

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Q: 1 I²+1 Estimate the area under the graph of f(x) = = rectangles and right endpoints. Rn = Repeat the…

A: The Right end point approximation formula is: ∫abf(x)dx=∆xf(x1)+f(x2)+f(x3)+...+f(xn) Divide…

Q: (r2 – 4xy – 2y2) dx + (y2 +4xy – 2x2) dy = 0 - Solve

A: To solve the differential equation.

Q: The car you are interested in has 16 color options, 3 engine choices, and 6 entertainment system…

A: Given ,  The car you are interested in has 16 color options , 3 engine choices , and 6 entertainment…

Q: Evaluate the function at the indicated value of x =1. f(x)=loggx 8 -8 - 1011 8 0

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Q: A polynomial P is given. P(x) = 2x³ - 11x² + 12x + 9 (a) Find all the real zeros of P. (Enter your…

A: We will find the roots.

Q: Determine the following general antiderivatives. [3x (x²-5)³4x [Axe+²7 tan(+²7) dx 10 d. cos(x)…

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Q: 구. ( 34 Cxtd) ax An 14 X? (X-1)

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Q: If √√x + √y = 10 and y(9) = 49, find y' (9) by implicit differentiation.

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Q: Evaluate f (x+3)(x-1) dx

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Q: Let f(x) = Va (2 – x)2. Use the local linear approximation of f (x) at ro V0.99 (1.01)?. 1 to…

A: To use the linear approximation for the given function

Q: 9. Sketch the region enclosed by the curves: y = x²-1, y = 3-x². Then set up, but do not evaluate,…

A: Area bounded by the curves :    If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on…

Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: x = 4…

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Q: Find the limit. If you L'Hopitals Rule, make sure to justify why you can use i use lim 2?e

A: We have to find the limit.

Q: b) c) dx x²(x²-16)2 S S- dx 1 (4x²+3)2 S. X = X = dx = dx =

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Q: Evaluate fx cos x dx

A: Solution:

Q: Consider the curve parametrized by x www = 1 + ln(t) and y = t¹ + 2t. dy a) First eliminate the…

A: topic - derivatives