Determine all possible values of 0, 0≤0 ≤2л, if cot 0 = -√3 cos²6 =1/12

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A: The tetrahedron is bounded by the planes Now, from above data limit of z is:-Now, we need to find…

Q: - Q1. Consider the function f (x) = − tan(x − π). a. Determine f '(x). b. Determine the slope of the…

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Q: Examine the graph of y = f(x) in the vicinity of x = c, and then select which statements are true.

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Q: lim In (tan.x) x→x lim In (cscx) X

A: 1) limx-pi- ln(tanx)2) limx-pi- ln(cscx)

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Q: 2. exp 2x²-8x+3 2 dx

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Q: Write the following in exponential form: y = In(0.34) O 3.4⁰ = y O e = 0.34 O e³.4 = y O 3.4 = e

A: The given equation is; y=ln(0.34)Write in exponential form.

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Q: 9. True or false: lim x = -1 X+1 1= x² 11 -IN 2

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Q: 4. (6) Evaluate the following limits if possible 1) lim x + 1 X-1 X²-1

A: Note:Since you have asked multiple questions we will solve the first question for you. If you want…

Q: Given at x = 5? X 0.9 1.0 1.1 h(x) 5.3 5.0 4.7 A. 3 B. 1/3 C. 1 D. -3 E. -1/3 what is a reasonable…

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Q: 2. m, ne N. (a) You are given that limx→ (x log x) lim [xm (log x)"] X→0 Use L'Hôpital's rule to…

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Q: 15-20 Use the method of cylindrical shells to find the volume of the solid obtained by rotating the…

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Q: Match each trigonometric function with one of the graphs. f (x) = tan z f(x) = cotr f(x) = secr =…

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Q: 4. A translation service has 74 employees. There are 45 employees who speak French and 22 employees…

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Q: Find | of ax 11 of and ay for the function f(x,y). f(x,y) = g(t)dt (g continuous for all t) X

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Q: Find the limits. (a) lim -t 10 t-x 5 + e-t (b) lim 1-2et t-∞ 1 + 3et (c) lim

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Q: Q9. Water is brought to a boil and then removed from the heat. The temperature, T, after t minutes…

A: Water is brought to a boil and then removed from the heat The temperature , T after t minutes is…

Q: 2. Differentiate a) each of the following functions. Leave in unsimplified form. b) f(x) =…

A: 2)a) y=x6+5 sqrt(x)b) f(x)=3sinx - cos4xDifferenciate the given functions.

Q: 3. The graph of f'(x) is given. Sketch a graph of f(x).

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Q: Determine the equation for the tangent to the curve f(x)=In(1+e') when the tangent is parallel to…

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Q: 2. Find the limits. Show your side work. 2 x-2 (x - 2)² (a) lim (b) lim tan x I→π/2- (c) lim tan x…

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Q: g(2,1, 2) dV over solid B. B = {(x, y, z) | 1² ≤ x² + y² ≤ 5², x ≥ 0, y ≥ 0,3 ≤ z ≤ 7} and g(x, y,…

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Q: For the functions w = 2x² + 3y², x= cost, and y = sint, express terms of t and differentiating…

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Q: Prove the following equations are identities for all permissible values of x, by manipulating only…

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Q: 3n (c) 201 n=1 Vn

A: To test the following series for convergence.

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Q: It is determinate because there is only one known force. It is determinate because there are no…

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Q: The population of a town grows at a rate proportional to the population present at time t. The…

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Q: Let D be the triangle in the xy plane with vertices at (-2, 1), (1, 0), and (3, 4). Describe the…

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Q: For the function f(x,y) = 6 of find and 8x+3y' dx dy

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Q: f=i-j g= 12i+ 3j Find: -4f-10g

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Q: 6. Determine values for a, b, and c such that the function f(x) = x³ + ax² + bx+c has a y-intercept…

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Q: The per capita growth rate of a population of cells varies over the course of a day. Assume that…

A: The per capita growth of a population of cells varies over the course of a day. Assume that time  is…

Q: 8. A laptop computer's battery has a voltage drop modelled by the function t V(t) = 20e 16, where V…

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Q: 4. A translation service has 74 employees. There are 45 employees who speak French and 22 employees…

A: This is question of calculusHere given conditionWe have to draw venn diagram for it.Further…

Q: (3) Let F(x) = — and g(x)=3x-5 F(x)g (x) 1) Find lim x +2 2) Find f(g(x)) and the natrual domain 3)…

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Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

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Q: Find the general solution of x²y" - xy' + y = x ln (x)

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Q: (x = 2+t 10. Given L₁: y = 1-t;t ER and L₂: F (3,0,-1) + s(2,3,-1); SER z = t a) Determine whether…

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Q: Use the fundamental identities to fully simplify sin (-2) cos (-2) csc (- S Enclose arguments of…

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Q: Find the solution to the initial-value problem dy dx 3xy(3+y), y(0) = 10 у),

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Q: 7. For what values of r does the function y = y" + 6y' + 8y = 0 ? erx satisfy the differential…

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Q: B Using the graph above, evaluate the following limit. lim f(x) 42- O PROF (A)1 (B) 2 (C) 3 (D) The…

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Q: Q7. If a beam of light that has intensity k is projected vertically downwards into water, its…

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Q: Calculate the derivativer(g(t)) using the Chain Rule. r(t) = (e¹, e¹¹,9) g(t) = 4t + 4

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Q: 4. The amount of radioactive carbon-14 left in a sample of biological material over time is given by…

A: The amount of radioactive carbon-14 left in a sample of biological material over time is given by…