Question 3. Let a € (0,1) and define f : T→R by 1 f(x) = sin(nx) na n=1 for all r E (-T, 7]. Prove that f converges for all x E T. (Hint: For r + 0, show E-1 sin(kx)< TanET: Then use Question 3 from the Midterm.) =D1

Q: Suppose f"(x) = (x + 2)°(x + 1)²(x – 2). Which of the following statements about the curv y = f(x)…

A: If f"(x) &gt; 0 , curve is concave up If f"(x) &lt; 0 , curve is concave down So only check the sign…

Q: 2. Show that by using MEAN VALUE THEOREM. u-v n >0 1+v2 3 <tan- < and deduce that 25 ww 4

A: First we have to show that v-u1+v2&lt;tan-1v-tan-1u&lt;v-u1+u2 where 0&lt;u&lt;v. Then we will show…

Q: Prove that (r) = tan(r) is uever negative in 0 <r< and show that g(x) = xsinr decreases…

A: We have to prove that f(x)=tanx is never negative in the interval 0,π2. We hence have to show that…

Q: sin - if x # 0 Ex: Let f: [0,1] → R such that f (x) 1 if x = 0 f satisfy mean value property and f…

A:

Q: Which of the following equations is FALSE? * O tan t = tan (t + 2m) where t n/2 + kTI O tan 2t = tan…

A: tant+2π=tant+tan2π1-tant·tan2π    ∵tanx+y=tanx+tany1-tanx tany=tant+01-tant·0=tant Therefore…

Q: 6. Say f(x) = 2x2² + cos x. Determine which of the statements below are true. (More than one may be…

A:

Q: 3. Find all values of a, b, c so that the following function is continuous for all values of x x-1…

A: Please see the below picture for detailed solution.

Q: 6. Find the intervals on [0,2r)where f(0) = sin²(0) is concave upward/ concave downw %3D

A:

Q: 2.6. Let ƒ be continuous on [0, a]. If x e [0, a], define fo(x) = f(x) and let %3D 1 fa+1(x) = -…

A: We will use the basic knowledge of integral calculus to answer this question. Note that we can only…

Q: Let f(x) = (c + 1)x+ In(cos x). For what value of c is f'(/4)=6

A: This question can be solved using the concepts of differentiation.

Q: Note: if you need to input infinity (0) or minus infinity (-∞) you can do so by inputting inf and…

A:

Q: 4 Juppose f is differentioble and we know that f'lx) s 3 for all x. It fro) =2, what is the largest…

A:

Q: Let a not be an integer, and f (x) = cos ax, x E (-7, 7] Extend f to PC (27). Show that 1 2 cot aT =…

A: Using Fourier series and putting some particular value to get our required series.

Q: Find the constants a, b e R so that the given functions are continuous on R. SO -22 + a, a sin ! +1…

A: A function f(x) is said to be continuous at a point  a if   limx→a-f(x)=limx→a+f(x) = f(a)

Q: + The f(x) = Vx – 2 defined at (-0,2] T F

A: Given: fx=x-2 A real valued function is said to be defined in an interval I, if fx∈ℝ, ∀x∈I. Now if…

Q: Find For the Following FunctIon XP 8x 2X8 22

A: we have to find dydx for the given equation.1. y=6z2+18x4-12x8differentiate w.r.t…

Q: 1- Calculate R6 for f(x) = 9 10x on interval [2, 4].

A:

Q: 2. Let r and y be real numbers be such x, y E {6i 3 2 2 3弧,T} T T T T (a) If 4 cos (2t) dt = find x.…

A: Here integral is already solved and answer is given in term of f(x) and g(y). Which is true because…

Q: Use the prové thát 1 x| < ]x| fór áll * # 0. onclü X| S x| för åll x € R. Hint. Apply MVT to f(x) =…

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Q: 3. (a) Let f(t) = t – sin t for all t. Show that f is a strictly increasing function of t, and…

A: f(t) = t - sint for all t  So, f'(t) = 1 - cost for all t  &amp;, f"(t) = sint for all t

Q: 2. Show that by using MEAN VALUE THEOREM 4-n < tan-1 v – tan-1 u < 1+v2 if 0< u<v 1+v2 3 <tan 25 -14…

A:

Q: 3. 6, Giraph of g'(x) Let fbe the function given by f(x) = (In x)(sin x). The figure below shows the…

A: For gx to be a increasing function, its derivative g'x must be greater than zero. From the given…

Q: Ex: the function f(x) = 2 * sin(x) = 2/4-1 is Zero for two values near x=-5. use bisection to find…

A:

Q: 1. Show that f(r) = sin(r + 3r) is equal to g(r) = -I Cos(I) at least once on -l. Hint: Think about…

A: