What will be the orientation of the curve of the graph of the function f(x) = on (-3,0)? A. increasing, concave up B. decreasing, concave down C. decreasing, concave up D. increasing, concave down

Q: VI. Determine the instantaneous rate of change of the function √x sin (³) In 2 = = [X² f(x): dt 1 +…

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Q: I. Evaluate the following limits x-tanx 1. lim x-sinx x-0 9

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

Q: Q3. Evaluate : .. . ܬ 1 ? 2 +y? dy ன்

A: We have to evaluate the given integral.

Q: 5. Use Cartesian coordinates to evaluate ㅋ yy dv where D is the tetrahedron in the first octant…

A: Let's evaluate given integral.

Q: -2 S₁² S₁² (²x²y^² + 2 (2x²y-² + 2y) dy dx 1 1

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Q: 3. A company determined that the price-demand and cost functions for selling x units of a certain…

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Q: Evaluate the following integrals 2x ·S- -dx 2 5+2x+x

A: We know that ∫duu = lnu+C ∫1v2+a2dv = 1a·tan-1va+C

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: a. Arc length of the curve y = 4- (x-2)² 4 bordering the region R

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Q: Write z, and z₂ in polar form. (Express 8 in radians. Let 0 ≤ 8 < 2m.) Z₁ = 4√3-41, 2₂ = -1 +/ Л 2₁…

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Q: √²2² √(-2² + 1)³ dz

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Q: Using the process shown in this unit, sketch the function y = 2x3 - 3x2 - 11x + 6, labelling all key…

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Q: consider the following. u=i+√√7j, v= -√7i+j (a) Find u. v. u'v= (b) Find the angle between u and v…

A: Solution is here

Q: In x 2. Use a local linear approximation of f(x) = 1+x² to estimate In (0.9) 1.81

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Q: A) Match each equality with the letter corresponding to the property it illustrates. Responses may…

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Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: Given that      Region R : 0≤x≤1 , 0≤y≤1-x2 , 0≤z≤4-x2+y2    Now, we take…

Q: 2. lim (tanx) (sin r-1) x→

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Q: Solve the differential equation dx 4x+6y+5 - dy 3y+2x+4

A: Concept: The general form of non-homogeneous differential equation  dydx=a1x+b1y+c1a2x+b2y+c2 Check…

Q: Given F(x) below, find F'(x). cos - Las () (1² - 2) dr F(x) =

A: Given.

Q: 312-3x| dx

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

A: Given

Q: solving the following differential equations (x + tany)dy=sin ey dx

A: On solving this we will get

Q: Jill burns 100 calories per hour while sleeping, 300 calories per hour while walking, and 200…

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Q: x-1 x² + 5x + 8 S dx

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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: Please

A: If d(t) is the distance object moved in time t.

Q: Evaluate 1₁-² 63 dx 1- cos (9x) 63 dx 1- cos (9x) - 7 cot 9x 2 +C

A: To evaluate the given integral.

Q: Find the coordinates of point C using the data given below. • Write your answer in this format : Y-X…

A: Concept: For the triangle ABC coordinates are       Y(m)             X(m)A    2784.57     3500.64B…

Q: A group of management students are creating a business plan for their proposed shoe brand…

A: Given problem:- A group of management students are creating a business plan for their proposed shoe…

Q: Q3. Evaluate : IL (2) * dy dx

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Q: [x xf (x²) dx Which integral is equivalent to the one shown: Oa) f f(u) du √uf (u) O b) S 2 O c) […

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Q: (3) Prove the Generalized Triangle Inequality: if a1, 42, ..., are R then an + Q2 + · · · + @ < 41 +…

A: Given

Q: Evaluate the double integral: y LL (Hint: Change the order of integration to dy dx.) dx dy.

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Q: Find the derivative of the following functions. g(x)=(x²³-3x²+1) -9x(x-2) (x²-3x²+1)* g'(x)=-

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Q: Evaluate the indefinite integral given below. Provide your answer below: f6e4 tan (2x) sec² (2x) dx…

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Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t² -…

A: Please refer to the image below

Q: Whatis the equation of the line that passes through (-3,5) and is parallel to theline 4x - 2y + 2 =…

A: The line passing through -3,5 and parallel to the line 4x-2y+2=0

Q: The 7th derivative of f(x) = 3x5 - 12x¹ + 7x³ − 11x² + √5 with respect to a is O 360T O none of the…

A: Topic = Derivative

Q: * (sin(2a) + cos(2x)) da Jo

A:

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: 3. -3 √₁|2 - 2³ | dr da 0

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Q: NUMBER 3 CLEAR AND SIMPLE

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Q: Evaluate the following limit, if it exists: lim x->1 = x2 + 4x - 5 / x-1

A: This question can be solved using the concept of limits.

Q: 2. 0 sec³ x tan x √2+ sec x dx

A:

Q: 5. Evaluate : p.v x² -∞0 (x²+3)² 8 dx

A: Concept: Some important integration formulas: ∫1a2+x2=1atan-1xa+C Where C is constant Reduction…

Q: Ex. Find the general solution to dy 1 -2.x dx X -

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Q: Test for exactness then solve. (6x + y2)dx + y(2x − 3y)dy = 0

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Q: Q2. (a) Write down the function corresponding to the graph given below. Is the function even or odd…

A: Concept: Fourier series: The enlargement of a periodic feature f(x) in phrases of a limitless sum of…

Q: I can't understand your solution.

A: Let's solve given integral.

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

A: