Evaluate the expression under the given conditions. sin(8 + 9); sin 8 = 8 in Quadrant I, cos 22√5 85 X = -23, in Quadrant I

Q: Determine Ex=1(-3)^-² its sum. O 4/7 5/7 O 7/2 7/4 the series converges and if so, find whether

A: On solving this we will get

Q: Evaluate the following limit, if it exists: lim x->7 = √x + 2 - 3 / x-7 (The square root covers…

A: In this question, we will evaluate the given limit expression.

Q: S t /1+3t - dt

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Q: Define R as the region bounded by the functions f(x): = 3 and g(x) = x + 1 between x = 0 and x = 1.…

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Q: Calculate the amount of money Cynthia had to deposit in an investment fund growing at an interest…

A: To find out the amount of money that Cynthia has to deposit.

Q: Given the following graph of f(x) , use your understanding of derivatives to sketch a graph of f'(x)

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Q: 3. Solve the differential equation of order one.  y' = csc x - ycot x STEPS: a. Put the equation…

A: Integrating factor of a differential equation of the form, dy/dx +P(x)y=Q(x) is given by, I.F=…

Q: (a) the volume of R using cylindrical coordinates with dV= r dz dr de where R: x≤ 1,0 ≤ y ≤ √1-x²,…

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Q: Find the area of the region bounded by the curves y = the x-axis using vertical strip. (x+1)2 y = 4…

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Q: dentify the surfaces of the following equations by converting them into equations in the Cartesian…

A: The given data is: To identify the surfaces: z2=4+4r2

Q: 3 sin³ (tan √x² + 3x²)] dx d [(x²+1) cotx dx 3- cos x csc x

A: To find the following derivatives.i ddx3 sin3tan x2+3x2ii ddxx2+1 cot x3-cos x csc x

Q: II. Evaluate the following integrals. 2. f (sin³x)√1 + cos x dx 플

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Q: 1. Use local linear approximation to estimate In (0.99). 2. Find the absolute extremum values of…

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Q: Use Cartesian coordinates to evaluate y²2 dV D where D is the tetrahedron in the first octant…

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Q: Determine the instantaneous rate of change of the function f(x) = [x² si sin (2¹) 1+√t x3 At x=1 dt

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Q: 4. Which of the following lines is parallel to y = 6x 18? 3x+6y=2 ○ 2x + 3y = −2 -6x -6x - 2y 2y =…

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Q: II. 3 4. 5- 10² - 0 + (0² + 0) dx S le* -e (e* e) e 0 Evaluate the followin

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Q: IV. A small business determined that the price-demand and cost functions for producing and selling x…

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Q: 3. -3 √₁|2 - 2³ | dr da 0

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Q: lim x++∞ x² + x e²x + In x

A: To Find: limx→∞x2+xe2x+lnx

Q: 1. (2x6x5 +7x³-3x² - 11) dx 2. f(9y2 +6y-4-y-5+1) dy (12x-x+x) dx 3.

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Q: II. Evaluate the following integrals 3. S 3* sech³ (3¹) -dx 1+tanh (35)

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Q: S √x²-25 dx X

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Q: 5x4y + y² 2x5 + 3xy' - dy dx O x¹y² + xy³ = 48 O x³y² + y³ = 120 о x²y² - y³ 3 = 56 O x³y² - xy³ =…

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Q: 5. Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis,…

A: Solution given below

Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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Q: Find the area (in square units) bounded by the parabolas x² + 2y - 8 = 0. a. 7.10 sq. units b. 7.01…

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Q: V. The velocity function of a particle moving along a horizontal line is given by v(t) = t² − 6t +…

A: Velocity

Q: Find the volume of the solid generated by revolving around the y- axis, the region bounded by 1 y =…

A: Solution given below

Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

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Q: 2 cos xsinx V2+cosx 1. S- -dx

A: Given

Q: Evaluate the indefinite integral given below. (10 (10-20x4) csc² (2x³ - 5x) dx

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Q: 4. Evaluate the double integral: L Lady. dx dy. 1/3 27 +1 (Hint: Change the order of integration to…

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Q: S 1 C=S²x + Sin'x

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Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: Evaluate the limit: lim (x - ln x)* x→0+

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Q: Use the first principles definition of the derivative to find f'(x) where f(x) = √x

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Q: The equation of a tangent line at a point (x₁, f (x₁)) where limh→0 f(x₁+h)-f(x₁) h = +∞ is x = x1.…

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Q: Evaluate the limits using the L'Hopital's Rule. lim (tan x)(sin x- x-1) x+2+

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Q: 3. +∞ 8 -∞ dx x² + 1

A: Given ∫-∞∞dxx2+1To evaluate the integral:

Q: Find the area bounded by the curve 2x² + 4x + y - 0 and the line y+x=0 a. 1.000 b. 1.125 c. 1.525 d.…

A: First we draw the graph,

Q: PLEASE SHOW COMPLETE SOLUTION.   Find each of the two areas bounded by the curves y = x^3 − 4x and…

A: Follow the procedure given below.

Q: 4x R is the region bounded by the functions f(x) = − ² + - +4-10 and 3 3 x² 10x 10 g(x) = - + Find…

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Q: 3.2.5 Test for exactness then solve. (x3+ xy2 − y)dx + (y3 + x2y − x)dy = 0

A: Given: (x3+xy2-y)dx+(y3+x2y-x)dy=0

Q: Using dA = dx dy, set-up the double integral that will find the volume of a solid bounded by z = 1…

A: We need to setup integral.

Q: a. A cylindrical container that is open at the top is to be made from two kinds of material. The…

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Q: 2. The position of a particle moving horizontally is given by s(t) = t³ − 6t² + 9t + 4, where s is…

A: s(t)=t3-6t2+9t+4   position when instance change direction means v=0…

Q: Evaluate the following integrals. 9x - 5 4. J dx 9x² 18x + 13

A: Given ∫9x-59x2-18x+13dx   Let  9x-5=αddx9x2-18x+13+β i.e.,    9x-5=α18x-18+β…

Q: 2.) Obtain the solution of the following initial value problem! (t-2)x' - x = 2(t - 2)², x(0) = 1.

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Q: (x + tan y) dy = sin 2y dx

A: