Find sin( ). (Hint: Use the half-angle formula.) arccos 3/10 V10/10 3V10/10

Q: Find the general solution of the equation and the specific solutions within the given interval…

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Q: Given: X1 = 1, x2= 3, x3 = -2, x4 = 4, Xs = 5. Compute (15) i-1

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Q: Q.3 Find general solution by separating the variables. i. y3 = (y* + 1) cos x dx. ii. y' = 3x²(y² +…

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Q: Simplify using either an Addition / Subtraction Formula or a Double Angle Formula, and then evaluate…

A: Solving the problem by finding the value of the expression.

Q: Consider the function f defined on the domain -0.5 s x s 0.5 with f(0) = 1, and 0.5 lim h 0 f(x+h)-…

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Q: 3. Scse*x dx

A: The objective of the question is evaluate the indefinite integral.

Q: b. S sech x = 2 Arctan(e*) + c

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Q: g (x) .5 Compute g(1) + g' (1) + g" (1) + g" (1) + g'

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Q: Answer the following True or False. If f(x) is integrable on a, b, then f(r) is continuous on [a,…

A: For the solution follow the next step.

Q: 4) represent the jollowing angles an higono metric cirde a7. + K2n 3. 4. c7 t. Eld

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Q: Write the first three terms of the sequence whose general term is an=n!3n. Provide your answer…

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Q: In xdx

A: Formula:Integration by parts:∫ uv dx =u∫v dx -∫ dudx∫vdxdxI=∫ x5 ln x dxu=ln x, dudx=1xv=x5I=ln x ∫…

Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.…

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Q: Find the area bounded by y? = x3, y=2x

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Q: 4. What is the geometric relationship between the two integrals below? et dx, In x dx Evaluate the…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: Consider the following planes. -4x + y + z = 4 12x - 3y + 4z = 16 (a) Find the angle between the two…

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Q: 2. Find the limiting values of 3x? + 5x-4 (i) as x → oO 5x? - x +7

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Q: 2. y = loga(x³ + 2x – 2)

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Q: 1- Vx 6 Find the equation of the tangent and normal to the curve f(x) at the point 4, 5 1+ X

A: Given:     f(x) = 1 - √x / 1 + x  Points: ( 4 , -1/5 )

Q: PROPER

A: We will solve this homogeneous differential equation.

Q: 3. * Sx² e** dx 1. pAx (8x? + 4х 1)+с C esx (8x? - 4х + 1) +С 16 16 1. 1. e** (8x2 + 4x - 1) + с 32…

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Q: 3 dt (2t +8) Vtti

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Q: 1. Find derivative, critical numbers and the absolute maximum and absolute minimum values of f(z) =…

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Q: What is the degree 3 Taylor Polynomial for sin x for a near T 지/2?

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Q: dy – (x - y + 1)?dx = 0

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Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: First simplify the integrand then integrate and simplify.

Q: Use the quotient rule to find the derivative of - 8 sin(r) +9 479 – 10 You do not need to expand out…

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Q: Find the gradient of the function at the given point. In(x2 - y) - 6, (2, 3) Z = Vz(2, 3) = %3!

A: To find out the gradient of the function at the given point..

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 3, 4) (b)…

A: Given: xyz=12 (1,3,4)

Q: What are the relative extrema of the function f(x)=x3+3x2-24x+7 a. relative minimum of -4, relative…

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Q: The functions f and g are continuous and differentiable with g(x) = f'(x). Selected values of the…

A: Given query is to find the average valu e of function g(x).

Q: 5. (xe*dx (1+x)2

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Q: If 0<c <d, then find the value of b (in terms of c and d) for which (x + b)dx= 0. b = (Type an exact…

A: Evaluating the definite integral and equating it to 0

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

A: Given query is to find the the population and rate of change of population after 20 years.

Q: Find a number within the interval [-5,5] such that the sum of the number and the square of one less…

A: Let, the number is x. The sum of the number and the square of one less than the number, S=x+(x-1)2

Q: Find the slope of the line that is tangent to the graph of f (x) 2a-3 at P(3/2, 0) О -3/4 O 2 O (E)…

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Q: power series representation for x³ s(2²) dæ ° cos (x

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Q: Direction: Find the differential equation of the family of curves described. 4. Ellipse with center…

A: Equation of ellipse is x^2/a^2 + y^2/b^2 = 1

Q: Evaluate the following indefinit 4. Ssin'x cos*x dx

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Q: 5. The solid below, known as Gabriel's Horn, is generated by rotating the graph of y = ! about the…

A: To find out the volume of Gabriel's Horn.

Q: 2. The growth rate (in inches per year) of the diameter at breast height of a certain tree is given…

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Q: Evaluate using Linear Equations. v(dx/dv)=6ve²"+x(2v-1)

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Q: 11 2

A: We can solve this as follows:

Q: Consider the function: f(x)=4−6x^2, −4≤x≤1 . The absolute maximum value is: And this occurs at x=…

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Q: b/ Find the solution to the homogeneous differential equation below dy x²+y² dx 2xy

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Q: S e2x sin 2xdx

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (17, 6, -3)

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Q: 1-cosx The value of limx→0 by using series is 1+x-e

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Q: A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is dissolved.…

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