2. Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are two distinct real numbers x1 and r2 such that f'(x1) = -f'(x2).

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A: suppose area be represented by AA= L×wA=(2t2-8)(3t+6)A=6t3+12t2-24t-48now differentiating on both…

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A: Use critical point to evaluate the absolute maxima and minima .

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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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Q: 21) Find tre fourth degree Taylor poly nomial Centned at C=4 for the function. m 7 (x)=In(x) Angues…

A: Pn(x) = f(c) +f'(c)x/1! +f"(c)x2/2! +.....+fn(c)xn/n! here we have to make upto 4 degree f'(x) = 1/x…

Q: A company determines that its weekly online sales, S(t), in dollars, t weeks after online sales…

A: S(t)=300etAverage weekly sales =13-0∫03300etdt                                 =13300(e3-e0)…

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: f(t) = -16t2 +385t +8 avg height from t = 5 to9.7 second f(9.7) =-16(9.7)2 +385(9.7) +8…

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A: Given

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A: limx→0+e1xusing chain rulelet f(x) =1xg(u) =eulimx→0+ f(x) = limx→0+ 1x =∞

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A: (6x-1)/x(x-4) it is very simple because in numerator there us multiplication given so A/x + B/(x-4)…

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A: for fixed point f(x) = x x = tan(x)

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Q: Determine the domains of f and g. x²(x+7) f(x)= , g(x)=x x² + 7x Domain of f: all real numbers x…

A: Domain:- The points where the function defined and exist.For rational function we have to remove all…

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Q: f(x, y) = R is the rectangle bounded by +1 -5<x<5 and 0<y<1.

A: Given function fx,y=1ex2+1Region R is bounded by -5≤x≤5 and 0≤y≤1.Surface area of over region R is…

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Q: simplify

A: We have to simplify  of the given expression

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A: Quotient Rule of differentiation :  ddx (uv) = v.dudx-u.dvdxv2. dxndx=n.xn-1

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A: a)β=10ln(10)lnI10-16β=10ln(10)lnI10-16β=10ln(10)ln(I)-ln(10)-16β=10ln(I)ln(10)+16ln(10)ln(10)β=10log…

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Q: What is the slope of the tangent line to the curve y=v(x-2) at the point (6,2)? 1/2 (E) None of the…

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Q: M3.2 Trigonometric Groups 3. S sin³x cos xdx 4. S Vtan x sec*x dx

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Q: 4y 1. Find all values of x such 49. Let F(x, y) = 2xy + 3x that F(x, x) = 0. %3D I

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Q: Let i = (6, – 6, 1) and v = (– 5, 5, – 6). %3D Compute the following: i · i = i. i = - 6(ü - i) = (–…

A: To evaluate the given dot product of vectors u and v.

Q: Let i = (– 4, 4, 5) and i = (6, – 3, – 2). %3D • Hint

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Q: Consider the following. 1 ifx = if x = 1 x²- 1 F(x) =

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Q: b) How many bit (or binary) sequences are there of length six with a 1 as the first digit?

A: A bit string is list if 0s and 1s For each of our 6 bits we have 2 choices 0 and 1