Use the definition of the derivative to find the derivative of, f(x)=6

Q: 1. Find the area of the shaded region. 3 y = Vx X 4 y = -x а.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first quest...

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Q: price p (in doi equation q = 800- 20p and 0s ps 40 (i) Express the revenue R as a function of q. (ii...

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Q: Find the derivative of the function. 10) y = (x + 1)2(x2 + 1)-3 2(x + 1)(2x2 + 3x - 1) (x2 + 1)4 -2(...

A: Given:        y= x+12x2+1-3

Q: 5. | sin (Tx) cos (Tx) dx

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Q: B. EXACT EQUATIONS Find the general solution of the following differential equations (1) (x² + y²) +...

A: Solution is given below:

Q: Let f(x, y, z) = x^2 - y^2 – z. Describe the level surfaces.

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Q: Figure 1 below shows the region R bounded by the curves y 4x, y =-4x and the line y =2. Determine th...

A: Given that, There is a graph between two function y2 = 4x, y2 = -4x and y = 2. We have to Find the a...

Q: 1.Determine the line limit {an} = 37 (2cos ! en

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Q: Figure 2 shows the shaded region S bounded by the curve x = y² – 2y + 1 and the line y = 3. Find the...

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Q: Let M(r, y) = y – cos y and N(r, y) = x sin y. Use the Green's Theorem to calculate the line integra...

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Q: Limits a. Find the limit: lim (x,y)→(1,1) (xy - y - 2x + 2) / (x - 1) . b. Show that lim (x,y)→(0...

A: Find limits   a. Find the limit: lim (x,y)→(1,1) (xy - y - 2x + 2) / (x - 1).b. Show that lim (x,y)→...

Q: Find the derivative with respect to x of f(x) = 2(x + 5)* + 3(x + 5)° + (x + 5)² + 4.

A: The given function, f(x)=2x+54+3x+53+x+52+4

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Q: Find the equation of the curve for which y" = x, and which passes through the point (1, 2) with (A 3...

A: Given y'' = x  and the curve passes through (1,2)  with a slope of 5/2. which means y(1) =2, y'(1) =...

Q: Find lim Itcos 2X メ 니(x- 폰) 2

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Q: x5tan(x²) sec²(x²) dx

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Q: Find the volume of the solid whose base is the semicircle y = V4 – x2 where -2 < x < 2 and the cross...

A: Explained below 

Q: 4 If f(x) = 4+ find f'(x). Find f'(5).

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Q: Suppose F(G(x)) = x³ and G' (1) = 5. Find F'(G(1)).

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Q: 1 (x² +2)% 3 4. Consider the curve y = 0<x<1 a) Find the length of this curve b) Find the volume of ...

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Q: (a) sec e = 2 e = degrees e = radians (b) cot e = 1 degrees radians

A: SOLUTION-

Q: 10. —бх2 — 12х — 10

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Q: Use the Linear Approximation to f(x, y) = V at (81, 16) to estimate 15.9 (Use decimal notation. Give...

A: Given:     f,(x,y) = √(x/y)      Point: (81, 16 )    Approximation : √(81.1/15.9)

Q: The function f(z) = 3 is represented as a power series 1- 4x 00 f(x) = Σ Cna". 0=t Find the specifie...

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Q: 10. Consider the poly (1, 2), (2,3) and the coefficients fo

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Q: Find the average value of f(x) = x² /57 + x³ on the interval [0,4]. favg = Report answers accurate t...

A: Find the average of the function  f(x)= x2√(x3+57) on interval [0,4] 

Q: b. e-Y sec² y dy = dx + xdy

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Q: There are 164 students in an Electronic Engineering (Computer) program where 110 students like Diffe...

A: Solved below

Q: Use your knowledge of the properties of logarithms to match equivalent expressions: bv log, (1) а. т...

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Q: Classify the number as a member of one of the following sets: the rational numbers, the integers, th...

A: NOTE: Refresh your page if you can't see any equations. . An integer is a whole number that can be p...

Q: (2) The number of women in the workforce, based on data and projections from 1950 to 2050, can be mo...

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Q: A. Sketch the graph of the function, not by plotting points, but by starting with the graph of a sta...

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Q: 2. Evaluate the following integrals using partial fractions. 1 (a) / dx (x – 3)(x + 1)² (b) / 6х? + ...

A: We know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C ; n≠-1 And ∫1ax+bdx=1alnax+b+C (a). Given: I=∫1...

Q: Let s(t)- 6t³ 721 + 270t be the equation of motion for a particle. Find a function for the velocity....

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Q: Find the total mass of a 5-m rod whose linear density function is p(x) = 3 + cos (Tx) kg/m for 0 < x...

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Q: - 5x + 7, find f(2). Use this to find the equation of the tangent line to the parabola y = 4x2 5x +7...

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Q: x' 3 3 4 27 -x+39 (2) For the function f(x)= (i) Determine the coordinates of the turning points. (i...

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Q: PAPER 1 4. INDICES AND SURDS N2014 page 25 (a) Solve the following simultaneous equations. 5* 25-2 =...

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Q: A. Sketch the graph of the function, not by plotting points, but by starting with the graph of a sta...

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Q: Let y = y (9-y), y(0) = y,, -0<y<∞ a) Sketch the graph of f(y) versus y b) Find the critical (equili...

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Q: 1. t seconds after jumping out of a plane, a skydiver's altitude (in metres) is approxi mated by the...

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Q: Use integration by parts to evaluate the integral: sin(In(9x))dx 1 x(sin (In)(9æ))– cos(In (9x)) + C...

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Q: b) Evaluate each of the following integrals: 2 i) | cos(2x)dx, 4x3 -dx. 1+ x* ii)

A: Explained below 

Q: 12. Given the graph of y = f(x) below, which of the following best represents the graph of y = (x +3...

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Q: Find the volume of a solid obtained by rotating the region under the graph of the function f(x) = :3...

A: We are asked to find the volume of the solid.

Q: Determine whether it is possible to express 1 as a liner combination of 1= m· 44 + n·91,. for some i...

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Q: Evaluate the indefinite integral. xp: V1-12 2 rcsin 2( 1- (2(1) 12 arcsin 2 1- x 2 X+C Basic Funcs T...

A: Given query is to eveluate the integral. We will use substitution to eveluate.