By an appropriate trigonometric substitution, Choices: √ √10 sin sin 0 cos de cos √10 sin 0 1 /10 -do VIO CO² 6 sin 0 do · V10 X sin 0 cos² Ode 10- x² -da is transformed into

Q: Consider points P(-1, 3), Q(1, 5), and R(-2, 8). (a) Determine vector PQ and express it in component…

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Q: The magnitude of the vectors and are 6 and 10 respectively, and the angle between them is 45°.…

A: The equation of the vector dot product is A⋅B=|A||B|cosθ, where θ is the angle between the vectors A…

Q: The linear approximation at x = and where B is: 0 to 1 X is A + Bx where A is:

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Q: Evaluate t

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Q: Determine the appropriate rotation formulas to use so that the new equation does not contain any…

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Q: Consider the function f(x) = = Let F(x) be the antiderivative Then F(x) = 7 3 x² x7 of f(x) with…

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Q: Evaluate the limit: lim 5 = x → 2

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Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: Suppose that fo f(x) dx = = 0-4 04 O 773 O 21 O 10 7 and ₂ f(x) dx = 3. Calculate f f(x) dx.

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Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.

A: We can find the answer in the following steps.

Q: 7. Differentiate w.r.t x- sin 5x cos 3x 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

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Q: 1 4. fv³ (a²-v²) dv

A: Given problem:- ∫v3a2-v212dv

Q: 1800 function Find the derivative of the following x3 F(x) = = 1²12²₁ = X5 (2t - 1)³ dt using the…

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Q: estimate the area under the graph f(x)=2x2+1   from x=0 to x=2 use four rectangle and the right…

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Q: [₁₁ ) If nd f*. f(x) dx = 4 and g(x) dx = 1, what is the value of ولاء f(x)g(y) dA where D is the…

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Q: Write an equation for the hyperbola shown in the graph y=-21 The equation for the hyperbola above is…

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Q: The processing time for the robogate has a normal distribution with mean 26 sec and standard…

A: Solution

Q: sigma 4-0 (1-x)/sqaurerootx dx

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Q: Evaluate 1 2. tht Htte tan e(:-+) 2 , у акуся, whve с is the contour given by

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Q: An object moves with velocity as given in the graph below (in ft/se How far did the object travel…

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Q: OS ng n Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of…

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Q: Consider the region bounded by x=4-y, the y-axis and the x-axis. 1 2 3 4 The volume of the solid…

A: Given:-

Q: Evaluate the following indefinite integral. 1 √ 3 ² + 8 - t dt =

A: Given.

Q: An applicant receives a job offer from two different companies. Offer A is a starting salary of…

A: Given problem:- An applicant receives a job offer from two different companies. Offer A is a…

Q: 3. Find the domain of f(x) = 1- 1 X X

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Q: 3. Find the domain of f(x) = 1- 1 X X

A: We have to find the domain of f(x)

Q: 2. Sketch the solution region of 2x - y - 1>0 (x - 5)² + (y + 1)² ≤ 25.

A: The given inequalities, 2x-y-1>0(x-5)2+(y+1)2≤25

Q: Evaluate ff (2x+5y+z) ds (2x+5y+z) ds where the surface S is given by S S: z=15-2x+3y, 0≤x≤1, 0≤y≤2.

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Q: Consider the region R bounded by the functions f(x)=3x and g(x)=x²+2. The area of R is: Choices: sq.…

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Q: Find the y-intercept of a quadratic function containing the following points: (2,5), (1,0), and (−2,…

A: First we need to find the equation of the quadratic function.

Q: what does the following integral equal? L 9(2)dz - [ = ['s g(z)dz = 23 and g(z)dz = 6.5

A: Given:             ∫-9-1gzdz=23              ∫-4-1gzdz=6.5              ∫-1-4gzdz=-∫-4-1gzdz

Q: Then S-4 -√25-x² 4xy dy dx = Graphs: sketch the region of integration and evaluate the integral.…

A: The objective is to  solve the above question.

Q: 2. √a²-x² dx x2

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Q: 6. If a = 2, b = 2√√3, y = 30°, solve for c and 3.

A: In a triangle, the given measures are a=2, b=23, γ=30°

Q: Test the series for convergence or divergence. Σ(-1) + ¹4ne-n n = 1 O converges O diverges

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Q: What is the domain of the rational function(x)=-3x²-16x +48 Oxe 31x*-4,-2.3.4) Oxe 31x*-4, 3, 4) O…

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Q: 2. f sin √tdt

A: To evaluate the given integral.

Q: Exams compri Question 6 a) Find parametric equations of an ellipse centered at the origin with major…

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Q: The sequence is given. Part A: Assuming the pattern continues, list the next four terms in the…

A: We have to find the solution .

Q: Suppose that P = f(t) is the population (in millions) of the country t years after the year 2000.…

A: Given that P= f(t) is the population (in millions) of the country t years after the year 2000

Q: Find the volume of liquid needed to fill a sphere of radius R to height h = R.

A: answer is in next step. please give a like!!

Q: Find the volume of a solid obtained by rotating the region enclosed by the graphs x = 2 - y and x =…

A: The given curves are; x=2-y and x=4-y2 Now find the point of intersection between the given curves.…

Q: What is the inverse of the function f(x) = 3(x + 2)²-5, such that x < -2? OF-¹(x)=-2+. 3 5…

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Q: II. Given a piecewise function f(x) = 2. 2x² + 2x " X log₂ (x − 1), x<-2 −2 < x < 2, x‡0 x ≥ 2. 1.…

A: The given piecewise function, fx=2,x&lt;-22x2+2xx,-2&lt;x&lt;2, x≠0log2x-1,x≥2

Q: 8) About the y-axis (0, 2) л y = 2sin (x) ;0< x≤ π X X

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Q: For each positive integer n, define an = n² sin 2 +∞o 1. Determine if the sequence {an} converges or…

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Q: Given that z dz= } 0 form. No rounded decimal number! 200 128 and 01:14:35 } z3 dz= 4, evaluate the…

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Q: Consider the smooth parametric curve defined by the equations = t (t²-3) { = 3 (t²-3) ¹ where t € R.…

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Q: Thank you! It's a little hard to read. If you don't mind, may you upload a picture?

A: Our Aim is to find two positive numbers satsisfying the following requirement given below:-The…

Q: plane. Use polar coordinates to find the volume of the solid below the paraboloid z = 18 - 2x² - 2y²…

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