Solve the following equations on 0≤0≤2π. 2 cos²x+3sin x = 3 tan²x-1= sec x

Q: -f=-9i+40j Find: -9f

A: Given vector: To find :

Q: Consider the Cobb-Douglas Production function: P(L, K) = 28L0.8 -0.2 Find the total units of…

A: To find the total units of production, we substitute the given values of L and K into the…

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = x³+y³…

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Q: If dy = x cos x² and y = -3 when x = 0, when x = π, y = -3.215 2 1.647 6

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Q: a- what is the difference between derivative of X^n and y^n (explain the followings: how many terms…

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Q: Let r(t) = (t², 1-t, 4t). Calculate the derivative of r(t) · a(t) at t = 5 assuming that a(5) =…

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Q: Evaluate the derivative (t'r(t)), where r(t) = (t¹0, t², t). (Use symbolic notation and fractions…

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Q: What is the area of the region bounded to the right by = by x = y²? 543-2-1 2 3 4 5 O co/ co/ col∞o…

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Q: Let f(x, y) = 125-3x²-2y2² Evaluate f(0, 3)

A: f(x,y)=sqrt(125-3x2-2y2)Find f(0,3)

Q: 5π Determine the exact value of sin- 12

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Q: 5. Find the equation of the tangent to the curve y = ex + x which is perpendicular to the line y =…

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Q: If an object is moving with v(t) = 3 cos(t) and the position X(0) = 1, what is the position of the…

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Q: The graph shows the velocity v(t) of an object. 4 3 2 1 0 1 O 13.5 O 14.5 O 15 2 3 O 15.5 4 V(t) 5 6…

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Q: The number of children in a church is increasing at a rate that is proportional to the number of…

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Q: Simplify the following expressions. sin x sec x sec² x-tan²x+cot² x sin² x cos 2x-cosx sin 2x+sin x

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Q: 26. Find a vector perpendicular to both ☎ = [1, 2, 3] and 5 = [3, 2, -1].

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Q: Suppose the position of a particle, s(t) is given by s(t) = t²8t+19 feet, where t is time in…

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Q: 6. The function f(x) is defined by the graph. State the value of each: c) lim f(x) = x →-1 d) f(4) =

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Q: 2. Differentiate each of the following functions. Leave in unsimplified form. c) 2x+5 y=-x² d) y =…

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Q: Use mathematical induction to prove that, for n≥ 1, n³-n is divisible by 3. Note: If you would…

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Q: Use a graphing utility to (a) plot the graphs of the given functions, (b) find the approximate…

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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: f(x, y) = √5x² + 3y² fz(5,-2) =

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Q: dy = x³ where y = 7 when x = 0. dx What is the value of y when x = 4 to significant figures? 12 15…

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Q: if f(x)= xe^x, determine f^(400) (x)

A: To determine the 400th derivative of the function f(x) = xe^x, we can follow a systematic approach…

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

A: Here, we need to determine the equation for the tangent to the curve f(x) = ln(1+e^x) when the…

Q: (a) Consider the first order separable differential equation (2x+3)(y² - 4) dy dx - (i) Find the…

A: Given that, the differential equation is                      (i)

Q: 3) lim x-1 f (x), where f(x) = |x-1| + 1₁ x 71 X X-2, XLI

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Q: 1. Indicate if each statement Is True or False. Write the word True or False not T or F. a) b) C) d)…

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Q: 4. How do we get the graph of y=-In (x+2) from graph of y= In (x)?

A: The function is

Q: Jane is taking a history class. The teacher states that the population of a country is shrinking at…

A: Size of the population, P = 10e0.5t

Q: Given f(x, y) =-3x¹ – 2xy² – 6y5, find - - fz(x, y) = fy(x, y) =

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Q: ' + y' - 6y = 3x - e2r y' е

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Q: Assuming - 2x³ + 4y² + 6xy = 0 defines y as a differentiable function of x, use the theorem dy dx -…

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Q: From first principles (that is, using the formal definitions of convergence and divergence) show…

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Q: Determine where the function is concave downward. f(x)= 1 x + 8

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Q: x= 1.079 is a solution for the equation ex = 12. O True O False

A: To determine whether the following statement is True or False. is a solution for the equation .

Q: Determine vector and parametric equations for the line with z-intercept 4 and is parallel to the…

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Q: 2. Which polar coordinate pairs label the same point? a. (-2, π/3) b. (2,-π/3) c. (r, 0) d. (r, 0 +…

A: We have to find the pair that labels the same point in polar coordinates.According to our guidelines…

Q: (-10,3) 23 (-2-1-0) -16 (-12,-3) (-8,0) (+3,-1)/ (-6,-5) 61 (1,0) (3,2) -6 (0, -1) (-4,-3) (5,0) y =…

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Q: For what value of the number k is the following function continuous at r=2 if x 2 f(x) = = (A) 3…

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Q: Use the graph of y = f(x) to answer the question. For what values of x is f(x) ≤0? -17 (-2,3)…

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Q: S sin x cos²x+cosx dx

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Q: Rewrite the equation with the variables separated. hh' = 6t²dt 0 h = 6t²dt dhe = tdt 6h ○ hdh =…

A: given

Q: Sex sin⁹⁹⁹ (e*) cos³ (ex) dx

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Q: Q8. The concentration of a certain prescription drug in the bloodstream after a single dose is…

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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)

Q: 2. Given that lim x-3 2 x² +ax+b x² + ax+b x²-9 2 lim x-4 the values and a and b. 2 x-9 and = 2,…

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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.