3 Using (14), show that a rotation around the x-axis through angle 8, is given by 1 0 R₂(0)= 0 cos ex 0 sin 0, cos Write down R, (,). Show explicitly that R, (0) R, (0,) # R, (0,)R, (0₂). 0-sin

Q: Determine f g a) f(t) = cos(t), g(t) = t b) f(t)=e¹, g(t) = e' sin(t)

A:

Q: Suppose f(x) = sin 4-x). Evaluate: x) dx (A - 3cos FC B -cos 3 X-4+ C 3 Cos 3 (D) 3cos -x- 4)+C

A:

Q: Sara draws the 4 of hearts from a standard deck of 52 cards. Without replacing the first card, she…

A: Given, Sara draws the 4 of hearts from a standard deck of 52 cards without replacing. a) we know…

Q: Let z=x+ iy with x and y are real. What is the imaginary part of sin (x + iy)

A:

Q: Prove that x2 cos x dx = T(2 – n) (+ sin æ)?

A:

Q: Consider the following. u = (2, 0), v = (5, 7) (a) Find u · v. U'V = (b) Find the angle between u…

A: Given that  The vectors  u=(2,0) and v=(5,7) To find the u.v and angle between the u and v

Q: f(i) = 5, f'(i) = -3i, g(i) = 3i, and g'(i) = 4. Find (fg)'(i).

A: Given fi=5,f'i=-3i,gi=3i,g'i=4. Find fg'i.

Q: Eliminate 0 from the equations : (i) x = h + a cos 0, y = k + b sin 0 (ii) x = a ser³ 0, y = b cot³…

A: Solution is given: Hope the solution is helpful.

Q: Where are the theta valuss for the horizontal and vertical tangent lines on [0,2pi) of r=1+cos theta

A:

Q: Find the derivatives of each of the following functions f(x)=-2 sinx b) y=-cos²x c) y = 3x sin x d)…

A: find the dervative

Q: Let i be the unit imaginary number. Thus i2 = -1. (1) Observe that the usual algebra rule to…

A:

Q: d dx d du d dz d [12 cos ¹2x] dy d dq [4 sec ¹3u] [10 tan-¹2z] [6 csc-¹4y] [9 cot-¹39]

A:

Q: 1+ csc x cos x + cotx

A: Given query is to simplify the expression.

Q: (6) Find дл ду : ye+sin(2)=423 (8 points)

A: Explanation is given below:Explanation:

Q: Q# (13 Rewrite: cos (x)sin(x)dx A) ſ u'du 1/2 B) Tu°du V312 C) [ -u°du 1 V3/2 D) [ u°du 1 V3/2 E)…

A:

Q: Find the direction field for the equation: y' = x + sin(y) + cos (x) at the point A = (0, pi3)

A: The direction field also known as slope field is used to graphically represent the solutions of…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A:

Q: (b) Determine all functions f=u+ iv that are analytic in the whole plane and has the property that…

A:

Q: Use the linearization of f(x) = sin x about an appropriate point Xo to approximate sin 610. Note…

A:

Q: X₁. (x₁, Yr) (x', y') 0 (x, y) X x' = x + (x-x, )cos-(y-y,)sin y' = y, + (x-x) sin 0+(y-y,) cos P' =…

A: Solution:

Q: y" - 2y y""y" + 2y = e2 (cosx-3 sin r). 21 - 4y + 4y = 5-e + c²r.

A:

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: If, for V = V (t), tsin(V) = cos(V)+ In(t), then: a) V'(t) = 1 – tsin(V) t(t cos(V) + sin(V)) b)…

A:

Q: Suppose f"(x) =Osin(3z) and f'(0) 4 and f(0) =-2 f(T/3) = Note: Dont confuse radians and degrees

A: