4- y 2- 4 10 12 -2- -4 (a) I f (2) da = 10 (b) f (x) dx = 12 (c) A f(2) da = -5

Q: 6. radians 7. radians 8. radians 2 3n radians 9. 10. 2n radians Example: -135' (OD)

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Q: 1. Determine the area under the curve y = x² + 5 from xX1 = 0 to x2 = 1.

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Q: Mass-Density Formula of a One-Dimensional Object. Given a thin rod along the x-axis over the interva...

A: We will find the mass. 

Q: Let g (x) = 12/x+ 10x . Use the limit definition of derivative to find the derivative of g (x) at 2....

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Q: Rewrite the statement in mathematical notation. (Let n be the number of cases of Bangkok flu and t b...

A: Given that - There are currently 200 cases of Bangkok flu, and the number is growing by 20 new cases...

Q: A man, 1.59 m tall is walking on a horizontal street at 2.5 kph away from a vertical street light, 2...

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Q: Find dy/dx, if y=(x^2+2)^4 (2x−3)^5 dy/dx = _______

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Q: S cos3 x sin* x dx

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Q: h" (t) = sec? t – Vt, h(0) = -3, and h'(0) = 3. %3D

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Q: Obtain the Taylor series expansion of the function f(x) = cot x centered at a 4

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Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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Q: (+e*)dx e* -In () 3.

A: Given that: ∫(x-1+ex)dxex-ln1xdx

Q: Find a set of basic vectors {ü, i} in R“ so that every vector in the solution set of the equations c...

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Q: Consider the graph of f(x) given below. (a) Analyzing the graph, if g(x) = f(æ), then g(x) is increa...

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Q: Suppose the cost of producing bananas is given by the differntial equation: dC/dx = 26/x + 45x whe...

A: The cost of producing bananas,dCdx=26x+45x

Q: Q4. (a) Evaluate the definite integrals: (i) ſ(2 – 5/1 – x² }tx_ (ii) [sin 2x cos 2x dx (iv) [": 'V1...

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Q: Evaluate the following definite integral: dx = 12

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Q: cion of the tangent line to the curve at the point

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Q: Find the distance between the point (3,-3,6) and the line X= 2+4t y=-4t z=-1+5t

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Q: Suppose that for each i such that 1 <i<N one has / f(1)dt = i Ji-1 What is / f(t)dt if N = 87?

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Q: Question Evaluate the following limit using L'Hospital's rule. (푸)( lim (cos(6æ))

A: We will solve the given limit by L' Hospital rule

Q: Find the derivative of the vector function r(t)=ln⁡(7−t^2)i+sqrt(8+t)j−5e^(2t)k r′(t)=⟨  ,  ,  ⟩

A: The given vector function is r(t)=ln(7-t^2)i+8+tj-5e2tk We have to find the derivative of the vector...

Q: On the graph of f(x) = sec x and the interval [0, 27), for what value of x does f(x) = –1? Choose al...

A: We have to find out 

Q: Question 1 A function F is an antiderivative of the function f on an interval I if for all x E1. A F...

A:

Q: Let a2 az A = | b1 b2 b3 C1 C2 C3 Suppose that det(A) = 3. Find the determinant of the following mat...

A: On changing determinant of row to corresponding column, there will be no any change on determinant.s...

Q: 4 – 2x dx. x3 + 2x2

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Q: 23T Does the angle 45 have a compliment? If so, what is its compliment. If not, explain why. Show al...

A: We can find the complement as below.

Q: 8x sin x y" + 4y/ + 5y = 8x sin x 1. ollowing econd ifferential equation:

A: The given differential equation is:y''+4y'+5y=8xsinx

Q: kf (x) dx =k ] f(x)dx Jas(a))dx=f (x) +C D

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Q: Objective: Determine the form of a particular solution for each differential equation. y" – 2y' + y ...

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Q: Evaluate  ∫√(1-7x^2) dx

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Q: 10 -10 At what values of x does ƒ (x) has an infinite limit (as x approaches this value)? Write down...

A: Given: To find at what value of x does f(x) has an infinite limit.

Q: Find the parametric equations for the tangent line to the curve x=t^2−1,y=t^4+1,z=t^4 at the point (...

A: Given: x=t2-1, y=t4+1, z=t4 Point 8, 82, 81, is for t=3 as you can see substituting it in the three ...

Q: 28. tan (2x) sec (2x) dx

A: follow the procedure given below.

Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing...

A: topic - application of derivatives

Q: 0.4 ソミーxe* -1 -0.5 1.5 -0.2 -0.4 2.

A: During calculation of integral,  Substitute x^2 = t

Q: The average change of a function f over an interval [¤1, x2] is f(x2)-f(x1) First find the average r...

A: We can find the instantaneous rate of change as below

Q: Question 19 Find the focus of the parabola 4x +24=8y-y?. A (-1,– 2) B (-3, 4) (-음4) D (-6, - 2)

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Q: Set up and evaluate the integral that gives the volume of the solid generated by revolving the plane...

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Q: e2x +2e* dx e* +1

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Q: S Vx2 – 8x + 25 dx

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Q: 57 37 Convert the point (p, 0, 4) = ( 5, 3 to Cartesian coordinates. Give answers 4 - as decimals to...

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Q: y = x, y = 3x; about the y-axis

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Q: QUESTION 4 Given f(x) = 8x³ + 2x. Estimate the value of ƒ(2.01) using differential. %3D

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Q: Question Evaluate the following limit using L'Hospital's rule. 1 lim 4x cos 6x4 Provide an exact ans...

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Q: What is the measure of the focal width of the parabola y+2y+4x-3=0 ?

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Q: 40. Working Mothers The percentage of mothers who work outside the home and have children younger th...

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Q: Question 15 Find the standard equation of the parabola with focus at (0, – 21) and directrix y = 21....

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Q: If f(x) = In( 3 + e4x ), find f '(0). f '(0) =

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Q: 3. /4(1-)esc (1-y)dy

A: We have to solve the integral