Given L f(x) dx = 16 and i g(x) dx = 8, Evaluate the following I [2f(x) - 3g(x)] dx

Q: Let f (x, y) = e(8x-9y). Find the equation for the tangent plane to the graph of f at the point…

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Q: y = 9 - t

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Q: Solve for x in the following expression using the quadratic formula. 3x2 + 19x – 4.9 = 0 Use at…

A: We can solve this as follows:

Q: S Vcos 20 sin 20 do

A: To evaluate the following integral.∫cos2θ sin2θ dθ

Q: The study of integrals in calculus is motivated by the problem of calculatin (a) the slope of a…

A: Study of integrals in calculus is motivated by calculating the area of a region bounded by curves.

Q: nvestigate the convergence of the following series. H.V 2n+5n 2) Σ-1 3n %3D1 1LJ!

A: We have to find out convergence

Q: Given the expression below, y = ecos arc sec(ln(r |- determine y.

A: The derivative is given below

Q: The marginal cost for a company to produce q items is given by MC(q) = 0.004q - 0.9q + 615. The…

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Q: Find the dimensions of a rectangle with perimeter 1000 metres so that the area of the rectangle is a…

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Q: S%3200000 e° find the growth rate of S.

A: Given query is to find the growth rate.

Q: Area A = 1,427 Calculate the definite integral f(x) dx by referring to the Area B = 2,460 Area C =…

A: Here we will find the definite integral,

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: I have stated the used formula in the solution

Q: Find the unit tangent vector T(t). r(t) = t2i + tj +4k , P(9, 3, 4) T(3) = Find a set of parametric…

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Q: Evaluate the integral. (5 – 2t + 3t2) dt |

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Q: Verify Green's Theorem by evaluating both integrals | y2 dx + x2 dy dA ду for the given path. C:…

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Q: 17. y dx — (х + бу?) dy %3D 0

A: To determine the solution of the given differential equation.

Q: 2 | (sin³x cos x + sinxcosx)dx 7/2 π

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Q: In sketching the graph of y=f(x) = – 3cos +)+4, we translate the graph of y = - 3cos s 5 by 4 units…

A: Transformation of graph

Q: In(1+x) -x cosx -1 1. lim x-+0 7- In(2x + 3) 3. lim x-00 In(5x -2)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20…

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

Q: The marginal cost for a company to produce q items is given by MC(q) = 0.002q -0.7q +620. The…

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Q: e2x 2.) S. dx ex – 5

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Q: Consider the points A(1, –3, 4), B(2, –5, 2), C(-1, –4, 2), and D(2,3, –5). (a) Find the volume of…

A: Let a,b,c and d are position vectors of point A,B,C and D resp. Therefore a=i-3j+4k b=2i-5j+2k,…

Q: y = (3+ e-2") V1 – e2al

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Q: dy 2 + y = 0, y(0) = -3 dt

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: r2 lim cos where k is - 00 - sec?! (A lim tan B lim - cos?- lim 2. 2.

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Q: 4. Perform the indicated multiplication of the two differential operators: (D –x)(x²D– 2x).

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Q: 11 ti + dt

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Q: 2. By differentiation rules , evaluate the derivatives of the following and simplify possible: c. y…

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Q: Suppose a product's revenue function is given by R(g): is units sold. Also, it's cost function is…

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Q: The distance traveled in the time interval 0 <t < 4 is given by the following. -4 r4 |t2 + 6t – 16|…

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Q: Two numbers have a sum of 72. What is their product if it is a maximum? (A) 1296 B) 1297 c) 1298…

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Q: Find both first partial derivatives. z = 15XVY 15xVy %3D dz az

A: We need to find partial derivative.

Q: 3. y = In? (csc2x). Find y"

A: y=ln2(csc2x)

Q: Solve for x. log x = - 4 0.0001 -0.0001 1.386 -4

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Q: Use the Newton-Raphson technique to find the value of a root of the equation e = sin 4x. An…

A: Given:

Q: 4r-10 (2r+2hlx-3-thb+20+C (2 + 2hk-3 +4hk+ 2) +C Option 1 Option 2 (भे+ 22 + 210l2 3/ 4Mly /2) 1 ८…

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Q: 3. Draw an example where ja + D|

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Q: 3x2+14x+13 x+4

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Q: Use series to approximate | V1+ x*dx correct to two decimal places.

A: Let's find.

Q: Find the divergence of the vector field F. F(x, y, 2) = In(7x2+ 6y? )i + 42xyj + In(6y2. + 72² )«…

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Q: Question 1 Which of the following is false? O yofe" = eu . Ine u (x) In e O yof log, u = u' (x) In a…

A: We can solve as follows

Q: 7. [x' In? x dx (9 In' x- 6 In x + 2) +C Ans. 27

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Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (5t + 6)i + tj, 0sts1

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Q: 1. Find all relative extrema and soddle points of the functon Use econd Partials Test where appli…

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Q: 4х Consider the function A(x)=2x+ for x > 3 Зx-1 (a) This function has one critical value larger…

A: We will start from critical points and follow upto inflection point

Q: Sing do Coso + Cose-2

A: LetI=∫sinθcos2θ+cosθ-2dθPut cosθ=uDifferentiate on both…

Q: įy'ny dy 2e' +1 Ans. 9. 13.

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Q: 4z² + 5dz 금(122+5) xo 4a? + 5 Part 2 of 2 ewrite the integrand in terms of u so that the integral…

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Q: 3. Compute f(x)dx 2х if x<1 f(x) = { 4 if x21

A: As we know from the property of the definite integral. ∫abfxdx=∫acfxdx+∫cbfxdx And The Power rule:…