Sf(x) – g(x) if f(x) ² g(x) lg(x) – f(x) if g(x) ² f(x) \f(x) – g(x)| %3D we obtain the formula \f(x) – g(x)| dx (2) which holds regardless of the relationship between f and g.

Q: f f(x)=x4 and g(x)=x3, then f′(x)=4x3 and g′(x)=3x2. The Chain Rule multiplies derivatives to get…

A: Given chain rule multiplies

Q: A- TI x + 2 x² – 3x – 10 51. f(x) x + 2| 53. f(x) : x + 2 х, 55. f(x) : x, xs 1 [x², x > 1 %3D x +…

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Q: f(x) = v3x _g(x) = 7\x + 6 h(x) = 9\x – 3 J(x) = 8x k(x) = -8/3x m(x) = x + 4 n(x) = 2\3x r(x) = v3x…

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Q: Increasing and decreasing functions Find the intervals onwhich f is increasing and decreasing.…

A: Given: fx=4-x2, fx=x2-16, fx=x-12 We know that any given functionfx is increasing in a interval if…

Q: ax-4 XX _4 f(x) = %3D Domain: Range: Continuity:

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Q: -343x x = -2 g(x) = { (x – 1)(x+ 2) x = -1 | a3 – 22 +1 , x + -2, –1 g(1) =

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Q: fx=å (3in (x*ry)-x2) %3D fy = Ly(31n (x*+y)-x2) %3D d fe-(3in (x*ry)-x2)

A:

Q: 1) F(x) = Vx+5 %3D x2-16 2x-8 2) h(x) = Vx2-15x+56

A: The domain of a function is the set of values which can be input into a function without the…

Q: f(x) = 3x + 5 g(x) = 4x² – 2 %3D h(x) = x² – 3x + 1 Find f(x) - g(x) – h(x). O - 5x + 6x + 6 O -5x +…

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Q: x2 – 1 6. g(x) = Vr – 3 at r = 4 - %3D

A:

Q: f(x) =x - &r +4 g (x) = 4x – 3 h(x) =x+2 1) (+g)(x) = 2) -h)(x) = 3) (hg)(x) =…

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Q: 2 Find [f(x) + 5g(x)]dx if 2 |f(x)dx = 8 and / g(x)dx = -1. -4 [f(x) + 5g(x)]dx = i -4

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Q: X1, X2 2 0 12. Minimise Z = 60x1 + 80x2 bo Subject to 20x +30x2 2 900 40x1 +30x2 2 1,200 X1, X220 LO…

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Q: %3| Find the value of k if the f(kx2 – 2x + 3)dx = 14.

A: Definite integration

Q: [5 < x < 8} 15<y<8S° f(x, y) = x² – 12x + y² – 8y on -

A: Given on . For global maxima and minima find the value of in given square region.

Q: 5. f(x) = 2x - 6 x2 - 7x + 12 Holes: Vert. Asy: Hor. Asy:

A:

Q: 9. If f (x) = e3*, then (f-1)'(x) = %3D 2 А. e3x e 3x 1 С. 3e3x 1 D. 3x B.

A: Given function is fx=e3x. To find: f-1'x Solution: To find inverse of the function, we will replace…

Q: [g(x )cx = 2 If then g(x )dx equals

A:

Q: d. yı = X1 X3 X1 + X2 Ya = - X1 – 3x2 – 2x3 e. yı = x1 + 2x2 + X3 Y2 = Y2 = x1 + x2 Ya = X2 + X3.

A: d)  The map from R3 to R2 is onto.  e)   The map from R3 to R3 is not onto.

Q: Sx² +2x + 1 d. h(x) = 15x – 1 - VRIGH 3x + 2 e. f(x) = {x +5 x² - 5 x 4 A VI

A:

Q: 1. f(x)=-2x²+x-1 a) f(0) =-| %3D b) f(-1)=- c) f(-x)=-X- %3D d) - f(x) = | e) f(x+1)=-3 ) f(2x)= -…

A: 1.    fx=-2x2+x-1   a) On putting x=0                         f0=-202+0-1      =-1  b) On putting…

Q: 16) g(x) = 4x - 5 s(x) = x' + x² Find (g + f)(-2)

A: Given,      g(x)=4x-5      f(x)=x3+x2

Q: -2 1 Find / f(x)dxif / f(x)dx = 2 and 3 -2 3 fro f(x)dx - 6. 1

A:

Q: 22. y = 3* 23.) f(x) = 24 fx) =x %3D + 4 2x + 3 g t) = - 7 fx) = 7x – 4 7x- 4 %3D 8(x) : %3D %3D

A: As per bartleby guideline for more than three subpart question asked only first three is to be…

Q: x" + 2x' + 8x = 2e-2t - e-t,x(0) = 1, x'(0) = 0

A: Given differential equation, x''+2x'+8x=2e-2t-e-t,x(0)=1,x'(0)=0 The objective is to solve the…

Q: 3) g(x) = x + 2 f(x) = x³ + 4x Find (g · f)(x) А) бх* - бх3 + бх? - бх 2x + 4x2 – 8x 4) f(x) = x² –…

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Q: In Problems 6–11, find the domain of each function

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: y = x(arctan x)² arctan (x+ (1+x²)arctan x) А. 1+x2 arctan (2x+ (1–x²)arctan x) В. 1-x2 arctan (2x+…

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Q: 4. t(x) = (x - 3)3 5. h(x) = -x² 6. f(x) = V=x 7. f(x) = 2x2 %3D

A:

Q: 0,x1 x+2,x<-1 f (x)= %3D 2,x2-1

A: Interval notation is a way to describe continuous sets of real numbers by the numbers that bound…

Q: If 0.3 is added to 0.2 times the quantity x − 3, the result is 2.5. What is thevalue of x?

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Q: f(x-1) e-2x+x² dx = O 1 -2x+x² e 2 2e-2+2x+C 2e-²x+x² + C e-2x+x² + C + C

A:

Q: 8) f(x) = 2x + 5; g(x) = 3x - 1 Find bo

A: Givenf(x)=2x+5g(x)=3x-1

Q: 2y''' - 3y'' - 3y' +2y =(e^x + e^-x)^2

A: We have to solve the differential equation  For which we first solve the homogeneous equation and…

Q: 5 Find (f(x) + 5g(x)]dxif -5 5 5 | f(x)dx = 8 and g(x)dx = -4. -5 -5 5 f(x) + 5g(x)]dx = i -5

A: The given integral values,∫-55fxdx=8 and ∫-55gxdx=-4

Q: 4+ V4x glx) = 2 A) g'(x) = (x + 2)° + 2 B) g "lx) = **2 5 x + 2 %3D E) g (x) = 1- 2r D) g (x) = 2(x…

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Q: x-e -2r -dx x²+e-2« *2(x-e-2«) A x²+e-2r xp- – 2(x-e-2x) dx x2+e-2r B -2x 2+e =21 dx x²+e-2¢…

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Q: f(x) = 5x -6 g(x) = 7x+ 12 h(x) 6x2 - 13x - 19 j(x) 3x2-x+ 26 k(x) = 11x – 9 m(x) = 8x2 - 13x - 34…

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Q: (a) yaf (x)-2x+1 (b) y-g (x)-(5 for x>0 (-5 for x <0 (0 for x-0 (c) y-h (x) -x+1

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Q: Compute f(x)dx 2x if x <1 4 if x21 f(x) =

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Q: -. g(x) = Vx + 7 i. Domain: (-7,00) Preview x + 30 . h(x) : 4 - i. Domain: (-30,4)U(4,00) Preview

A: Given query is to find the domain for the function.

Q: -2x X-e -2x x+e * 2(x-e-2*) A -2x xp- x²+e¯ -2(x-e-2*) B x²+e =² -2x -2x e dx -2x x²+e-2r x²+e=2« D…

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Q: 2 f(x) = x² - 9 %3D (- 4,f(– 4)) = (0,f(0)) = (4,f(4)) =

A: Given that  f(x) = 2/(x2 - 9)  We need to find the following points. Now, f(-4) = 2/((-4)2 - 9)…

Q: 19.yf(x) = 2|x – 1|; f(-2). f(0), f(¿). f(2), f(x + 1), f(x² + 2)

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Q: e) (f-g)(-4)= %3D

A:

Q: Solve for (f o g)(x) , when x = -1 f(x) = 5x + 1 g(x) = 3x - 4 Solve for (g o f)(x) , when x = -1…

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Q: 1. Find fog. f (x) = -4x + 6 A) (fog)(x) =-5x B) (fog)(x) =-4x² + 30x – 36 C) (fog)(x) =-4x + 30 g…

A: f(x)=-4x+6g(x)=x-6

Q: 1. f(x) = 3x^3 -2x^2 -4x +1; g(x) = -5x +6x^3 -2 +x^2 . Find (g-f) (x). * %3D -3x^3 -3x^2 + x +3 O…

A: Given: f(x)=3x3-2x2-4x+1g(x)=-5x+6x3-2+x2 To find (f-g)(x)

Q: 4. f(x) = 10-5x² 5. f(x) = e[ 6. f(x) = /In(e 3x + a³x) %3D

A:

Q: Find the derivatives of the given functions. (Part D and E)

A: d)  We will need the quotient rule. For that assume u and v and find u' and v'