All parts of this question concern the function f(x) = 6 sin x + 7 cosx. (a) Find the smallest positive constant M that satisfies M2f) (t) for every possible combination of an integer k20 and an evaluation point t€ (-∞, +∞o). Hint: A standard trigonometric identity implies that, for a certain angle d. one has f(x) = √85 sin (x+) for all real x. Answer: M = f(n+1) (t) (n+1)! In both parts below, estimate En(a) using Lagrange's formula with the constant M found in part (a). (Use technology as required.) Recall the standard decomposition f(x) = T₂(x) + En(x), in which Lagrange's formula says En(x) = (b) Find the smallest n for which the polynomial value T₁, (0.4) provides an approximation for f(0.4) that is guaranteed to be accurate to within 10 decimal places: Answer: n == -x+1 for some t between 0 and x. This valid for every integer n 20. Hint: To guarantee D correct digits after the decimal point, accounting for rounding, one must have |E, (0.4)| ≤ 0.5 × 10-D. (c) Suppose n = 7 is prescribed. Find the largest positive number a such that the approximation T7(x) for f(x) is guaranteed to be accurate to within 8 decimal places, for all in the symmetric interval (-a, a). Answer: a =

Q: number who have not heard it, determine an equation for the number of students who have hear the…

A: We have to find out the equation of the given problem.

Q: Determine the exact x– value(s) of the intersection points of the functions f (x) = 4 sin² +7 sin 4…

A:

Q: Va? – x²

A:

Q: Consider the following function. x³ √√²-2² 36 dx (a) Determine an appropriate trigonometric…

A:

Q: Determine two unique values of θ in the interval [0,2π), such that                    sec (θ) = 2√3/…

A:

Q: ) Use Euler's formulas to calculate | cos(ax) sin(bæ)dx for a > 0 and b > 0.

A:

Q: Let x be a real number between 9 and 11. Provide an expression for sin(cos-(x - 10)) (in terms of x)…

A:

Q: Which of the following function is not harmonic in the C-(0): Select one: COS Z o Im ( O Re() sinz o…

A: Let f(z)=u(x, y)+ιv(x, y) be a function where z=x+ιyHarmonic Function: A function u(x, y) is called…

Q: Which is the exact value of the trigonometric expression sin 2-2 F H 2+ 1+ G J 2. 2. 2.

A:

Q: Find the exact value of trigonometric expression given that sin (u)= -3/5, where 3pie/2 <u< 2pie,…

A:

Q: 1) Use Excel to plot both of sin(x), cos(x) at the same plot, where: 0<x <2n.

A: To find- Use Excel to plot both of sinx, cosx at the same plot, where: 0 ≤ x ≤ 2π.

Q: 9. Let a, b, and d be positive integers. Prove that if (a, b) = 1 and d divides a, then (d, b) = 1.

A:

Q: The following represents the graph of which trig function: UU 2- -2 n 3 n 2 2 sin(x) O sec(x)…

A: according to given graph  The  given graph is csc(x) graph

Q: interval Answer in radians. Type pi for . the following expressions. Beca ㅠ [27] (a) sin ¹(1) (b)…

A: The given expression is To evaluate the given expression in the interval is .

Q: If sin(x) = 1/3 and sec(y) = 5/4, where x and y lie between 0 and x/2, evaluate the expression using…

A:

Q: Find the recursive formula of the following sequence. (4, 7, 15, 24, . ... a1 = 4, a, = an-1+ 3(n +…

A:

Q: Use the triangle below to answer the questions. Assume x and y are positive. 0 10 (a) Express x as a…

A:

Q: Evaluate 2 sin x cos x dx by three methods: (a) Let appearance of the answers obtained in (a), (b),…

A: To evaluate: I=∫2 sin x cos x dx

Q: 6. cos COS 7π 6

A: The given expression cos-1cos7π6. We have to find the value of this expression.