5. The velocity function (in meters per second) is given for a particle moving along a line. Find a) the displacement b) the distance traveled by the particle during the given time interval. v(t) = t²t,0 ≤t≤3

Q: Determine a definite integral that represents the arc length of = 2 cos(8), 0 ≤ 0 ≤ H2 2 do

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Q: 2. a) Evaluate the integral. sin(3nt)dt b) 2x³ +3x6 dx

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Q: Let F(x, y, z) = xi + yj + zk. Evaluate the integral of F along each of the following paths. (a)…

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Q: Determine whether the lines L₁ and L₂ are parallel, skew, or intersecting. L₁: x = 9 + 6t, y = 12 -…

A: We have to find that given lines are parallel interest or skew.

Q: 33 ow your work and explain, in your own words, how you ar relevant explanations may receive reduced…

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Q: Determine a definite integral that represents the area of the region enclosed by one petal of r = 4…

A: We have,      r = 4 sin (3θ)       a = 0

Q: Question 4 Given that sin() = 0.73, match each trigonometric function with its value. cos(8) csc (8)…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given graph about the…

A: We have, y=x2 , y= 2x, about the line x= -1

Q: Suppose that R is the finite region bounded by y = x, y=x+2, x=0, and x = 4. Find the exact value of…

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Q: 7. Sketch the region enclosed by the given curves and find its area. y = sin x, y = cos x, x = 0,…

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Q: 12. Sketch the region bounded by y = √4-x2 and y = -√4-x² for-2 ≤ x ≤ 2. Give a definite integral…

A: We have to sketch the region bounded by…

Q: consider the region bounded by the parabolas: y=x² + 4x + 3 and Find y = - x² + 2x + 3 the area of…

A: The region bounded by the parabolasy=x2+4x+3 and y=-x2+2x+3

Q: Sketch a graph of the function sin(x-45°) + 2. Please state the range.

A: Let f(x)=sin(x-45ο) + 2

Q: Let ux² then dx = du 2x and so 2 2 du S ƒ ze²³d² = ƒ re² de S xe dr xe" 2x 0 0 1 S = (²-1) e" du

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Q: 1/3 The integral fo²³ 3-√2-9x1² dx is to be evaluated 0 directly and using series approximation. 1)…

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Q: Let f(x)= - (2.-17). a. Use the following definition of the slope of the tangent line at x = a to…

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Q: 7. (1 point) An object starts from rest at the point P(1,2,0) and moves with an acceleration of a(t)…

A: Given an object starts from rest at the pont P(1,2,0) and moves with an acceleration of a(t)=j+2k.…

Q: 2. Consider the function: a) Determine the derivative. y = 2sinx b) Calculate the exact value of x…

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Q: Evaluate the double integral circles x² + y² = 9 and x² = 9 and x² Answer: SSR y² -dA, where R is…

A: To evaluate the given double integral use the following substitution. x=rcosθ y=rsinθ x2+y2=r2

Q: The force F has a magnitude of 310 lb and acts along the diagonal of the parallelepiped as shown.…

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Q: If f is a differentiable function and f'(x)=x4 point at =x²+2x³ - 15x²2, then f has an inflection 3

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Q: A man gets a job with a salary of 31800 dollars a year. He is promised a 2780 dollars raise each…

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Q: z³dz /4 – z²

A: To perform the indicated integration by using Rationalizing Fractions. ∫z3 dz4-z2

Q: Find the area of the region enclosed by y = 3.25x and x = 7.5-y². 2 2 1 2 w A 5 6 N Use horizontal…

A: The area bounded by the curves x= f(y) , x= g(y) between y= a and y = b is given by A = ∫abfy-gy dy

Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y₁ x = s + 2t - u, y = stu²…

A: z=x4+x2y, x=s+2t-u, y=stu2 given s=1, t=3, u=5

Q: Solve the given differential equation by separation of variables. dx + e³xdy = 0

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Q: Find the area between the curve y = y 2.0 1.5 1.0 0.5 1 square units y = 2 1 x5/4 1 X5/4 3 and the…

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Q: In a particular city, taxicabs charge passengers $2.20 for entering a cab and then $0.50 for each…

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Q: Find a parametrization of the line in which the planes x+2y + 6z= -1 and 2x + 3y +9z = -3 intersect.…

A: Solving the problem

Q: Find f. f"(x) = 1 - 6x + 48x², f(0) = 1, f'(0) = 2 1.

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Q: . Use a table to find the Taylor Polynomial P;(x) for f(x) = cos(x) with center c = π. A. P(x)= B.…

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Q: Find f(x) by solving the initial value problem. 5 f'(x) = 1 +e²+ = f(1) = 7+e f'(x)=1+e*+

A: Given: f'(x)=1+ex+5xf(1)=7+e We are required to find: f(x)

Q: Determine whether the three points P = (-5, -4,-3), Q = (-8,-10, -12), R = (-11, -15, -21) are…

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Q: which value (s) {5,7,9,11,13}make the inequailty w-4<8 true?

A: The inequality is given and we need to solve it.

Q: Suppose 4²x = 12. Then x = A. In12 OB. (√12)³ 3 OC. 3 D. 109412 E. 09122 2

A: 1). logbxa=a·logbx  where x,b&gt;0, b≠1 2). logbb=1

Q: A bucket begins holding 15 kgs of sand. The bucket is to be lifted to the top of a 20 meter tall…

A: Initially sand present in bucket = 15 kg,Bucket leaks 0.2 kg/m sand when it is lifted.

Q: (b) Determine the following integrals: 3 (i) S. 2 x x² - 1 dr

A: As per our guidelines we are supposed to answer only one question at a time. So only solution of…

Q: J 2x cos(x²) esin(x²) dx

A: Integration of  2x.cos(x2)e^sin(x2)dx  We have to calculate du after suitable substitution

Q: 9. The region R enclosed by the curves y = √√x and y = x² is rotated about the x-axis. Find the…

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Q: f(x, y) = e cos(ly). Find and classify all critical points of the function. If there are more blanks…

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Q: Find an explicit solution of the given initial-value problem. x2dy dx =y-xy, y(-1) = -4 y =

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Q: Find two unit vectors that make an angle of 60° with  v = 3i + 4j.

A: We are required to find: Two unit vectors that make an angle of 60° with  v = 3i + 4j.

Q: A tumor is injected with 0.82 grams of Iodine-125. After 1 day, the amount of lodine-125 has…

A: Law of Decay is given as  P = P0e-kt where P is the amount after time t  P0 is the initial amount  k…

Q: f(x) = 8+x 8 - x on [4, 6].

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Q: Q6 Use the graphs below to fill in blank. Write DNE" for Does Not Exist" or NEI" for Not Enough…

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Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

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Q: 3. Determine the absolute extreme values for the function Y=3sinx + 4cosx on the interval [0,27]

A: y = 3sin x + 4cos x ,on the interval [0, 2pi]

Q: 3. Differentiate the following exponential function without simplifying f(x)=√(e*)(2x)

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Q: Use implicit differentiation Find dy at the point (1, 1) for 7x² + 4y³ + 6xy = 0. dx 10 9 10 to find…

A: given 7x2+4y3+6xy=0 , point is (1,1)

Q: Find a formula for a cubic function f if f(3) = 24 and f(−1) = f(0) = f(4) = 0.

A: