Find the general solution to the differential equation y = x¹ tan(y) y = sin-1 [cer³15] Use the letter "C" for any constant of integration. A help (formulas)

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: Find the solution to the initial-value problem dy dx 4x = y²e¹* sin(2x), y(0) = 1

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Q: 1. Determine vector and parametric equations for the line with z-intercept 4 and is parallel to the…

A: To determine the vector and parametric equations for the line with -intercept 4 and is parallel to…

Q: 3. Find the slope of the tangent to f(x)=x√√2x² + 17 at the point on the curve where x = -4.

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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: :. Calculate the total amount of interest earned from this investment during the 4-year period.

A: The amount invested, P=$13000Interest rate, i=5%Compounded frequency, m=2 (semi-annually)

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: 9-14 Use the method of cylindrical shells to find the volume generated by rotating the region…

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Q: Find the Volume V(S) of the solid S generated by given R: R is the region bounded by -x²+9 and…

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Q: Q6. The population of foxes in a provincial park is modeled by the equation P(t)= +40, where t is…

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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: Given f(x, y): fz(2, 3) - fy(2, 3) = -4x¹ +5xy² + 2y³, find the following numerical values:

A: The given function is; f(x,y)=-4x4+5xy2+2y3Find fx(2,3) and fy(2,3).

Q: 5. Let G(x) = = = f* tan-¹(s) ds x2 Find G'(x)

A: Fundamental theorem of calculus

Q: Determine whether each of the following series converge or diverge, using any of the standard tests…

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Q: 2. Determine the derivative of the function f(x) = 2x² ecos 2x Express you answer in simplified…

A: Given :-  The function To Find :-  The derivative of the given function.

Q: find the integral sinh sinh?(5t)cosh?(5t) dt

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Q: tan x2 x dx (Hint: Start with integration by parts.)

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Q: dy dx = (y +9)(y-9), where y(0) = 8 The partial fraction constants in the partial-fraction method…

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Q: 3a) Determine whether or not the function below is differentiable at O by using the definition of…

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Q: So dx 1+√√3x 3x - 2

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Q: What is the general solution to √æ² +3¹² = 2x ? dz Oy= 2√²+3+C Oy=√√√²+3+C Oy=C√√√x² +3 Oy= 2√x²+3+C

A: given

Q: Find the solution to the initial-value problem dy dx e5y. 3, y(0) = ln(ln(3))

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Q: 2. Determine the absolute maximum and minimum values of f(x) on the interval -2≤x≤05. Decimals…

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Q: 5. Which equation can be solved by referencing the graph below? -1/2 -11/4 3 cosx – 1 = sinx O…

A: The range of both cosine and sine function is .The value of the sine function is zero for all…

Q: Find all the second-order partial derivatives of the following function. w=5ye3x² - 4y

A: w= 5ye3x^2-4yWr have to find all second order partial derivatives

Q: The plane x + y + 2z = 10 intersects the paraboloid z = x² + y² in an ellipse. Find the points on…

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Q: Find the location at t = 3 of a particle whose path satisfies 5 = (18r - (+12+ 21-4) (t 1)² dr dt…

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Q: If a population P is growing at a rate that is proportional to √P, is the population growing…

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Q: A region bounded by f(x) = Væ + What is the volume of the solid formed by revolving the region about…

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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: The velocity of a particle on the x-axis is given by the differential equation dx d=³√t, The…

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Q: 6. Determine the equation of the tangent to y = :-xex + ex at x = 0.

A: Explaination of the answer is as follows

Q: Find the Volume V(S) of the solid S generated by given R: R is the region bounded by x²+y-4=0 and…

A: To find the volume of the solid S generated by revolving the region R about the line x=-2, we can…

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz+zx, Po(1,-1,-2),…

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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…

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

Q: Many populations are facing negative growth rates. If the population of the Ukraine was 60 million…

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Q: Let f(x,y) = x² − xy + y² − y. Find the directions u and the values of Df(1, -1) for which the…

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

A: If a beam of light that has intensity k is projected vertically downwards into the water its…

Q: Evaluate the line integral Jc (2x³y³) dx + (9x³ + y³) dy where C is the unit circle, and verify…

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Q: S 6x²+5x+1 x³+3x²+2x+6 dx

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Q: What is the equation of the curve that passes through the point (1, 2) and has a slope of at any…

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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: Given the Pythagorean theorem a² + b² = c² where a and b are the lengths of the perpendicular sides…

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Q: calculate 1.100 1/2 dz, and 1100 1/2 dz x² x²

A: Solution- We know n=-2

Q: Consider the integral integrals: 3 -y ³³ f(x, y)dady. If we change the order of integration we…

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Q: Determine the exact value (no decimals) of the slope of the tangent line to πT f(x) = −2 sin x at…

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Q: Find the Jacobian for x = u²+ 10uv and y I VITETNE limmstan guv²

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Q: 20. If f'(r) exists at r= a, then (A) True (B) False lim f(x) = f(a) PTA

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Q: Which of the following is a solution to sinx+cos(3x)= 0.927 pi/4 1 pi/2

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Q: 4. Which of the following statements are TRUE about how y=-4 arcsin a ( 3² (x+5)) + 6 I. Vertical…

A: We have to define the transformations required to get the given function from its parent…