aduction to Calculus in Physics: ulus is a powerful tool used in all areas of physics. One of the initial applications areas is classical physics, particularly Newtonian mechanics. An important function is the position functions (t) that measures how far the object is from point 0 at time t. The question w deals with just the position functions (t). plem Set question: position function for a falling objects is given by s (t) = -16t² + vot+so, where s (t) is the height of the object in feet, up is the initial velocity, so is the initial height, and it is the time in seconds. Il is shot upwards from the surface of the earth (so = 0) with an initial velocity of 65 feet per second. What is the maximum height reached by the ball? nd your answer to the nearest integer. maximum height reached by the ball is

Q: 2/ Reversing the order of integration fxsinydydx.

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Q: Find an explicit solution of the given initial-value problem. √2 √1-y² dx - √1-x² dy = 0, y(0) = 2 y…

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Q: Q3/Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

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Q: Find the general solution of the given differential equation. 2 dy dx - + 6y = 3 y(x) = Give the…

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Q: First use appropriate properties of logarithms to rewrite f(x), and then find f'(x). f(x) = 2 In…

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Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = x sin x n = 1 f'(x) n = 2…

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Q: a) Graph the function f(x)=2x-5x + 3. b) Draw a tangent line to the graph at the point whose…

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Q: Find the greatest common factor and least common multiple of A, B, and C. Write your answers as a…

A: We need to find G.C.F. , H.C.F.

Q: Determine the orientation of the concaves of the following function

A: See the answer below

Q: Let x + 1 f(x) x + 6 ƒ−¹( − 2) = - =

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Q: Find the values of x and y - SX+(s+6) Y=1 (3-s) X-2sY= -8 ..... (1) (2) ...

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Q: Solve the following exponential equation. ex + e- x = 6 Select the correct choice below and, if…

A: According to question,Given equation,ex + e-x = 6

Q: [ (cosx+2sinx) COSX dx

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Q: To find the volume formed by the function z=f(x, y) = x²y over the triangular region bounded by the…

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Q: (b) y = e, y = ²x, x=0, x= ln 2 1 (c) x = =, x = 0, y = 1, y = e Y (d) y = 5x - x², y = x (e) y =…

A: Using vertical strip

Q: The value of V(-25) is * О -5i 4i 5i оооо О -4

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

Q: 35

A: Please refer to the image below

Q: Example 5: Use double integral to find the are

A: In this question we will use basic concepts of double integration to get the required area bounded…

Q: (1+x)*dx X

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Q: Which of the following represents the difference quotient for f(x)= -²₂ 2 x(x+h) 2 x(x+h) 2x+h…

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Q: A function f and a point P are given. Let correspond to the direction of the directional derivative.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

A: I am attaching image so that you understand each and every step.

Q: Q3/Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

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Q: Q2: Find y(2) if D.E as give dy 2+3y=sin 2x, y(0) = 6 dx Given

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Q: 2. Evaluate the improper integral S₂ (5. dx (5-x)4/3 or state that it diverges.

A: The given integral,      ∫28dx5-x43

Q: A large tank is filled to capacity with 600 gallons of pure water. Brine containing 2 pounds of salt…

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Q: Direction: Solve the following problem of bounded areas, marks for complete work out and mark for…

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Q: Solve for x. log 3(2x-5)=3

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Q: * The following function f(x) = x^4 sinx is odd о neither O O even

A: Replace x with -x

Q: Consider the function f(x)=2sin(x)+(√3/2) x^2 This function has two inflection numbers A<B in…

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Q: following

A: We have to find the value of the given condition according to the given information

Q: Let Z1 = 3 + i and Z2 = 5+2 i. Find 2 Z1 / (Z1-Z2) - (14/5)-2 i O (14/5) + 2i O O O - (14/5) + (2/5)…

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Q: Solve the differential equation (24xy +24y²) + (8x² +24xy)y' = 0 using the integrating factor u(x,…

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Q: Rewrite the given function with a rational exponent. 7|X 8 = y In X + 8 = In x + 1 || In x + 00 8 00

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Q: Determine whether the function is one-to-one. If it is, find a formula for its inverse. f(x) = 9 x+1…

A: Equate fx=fy and determine whether the given function is one to one.        fx=fy…

Q: ---(1) (y-2)² + (x - 1)² - 9 ---(2) 3. 16 = x² + y²

A: use for quadratic equation   a x2+bx+c=0x=-b±b2-4ac2a and -1  = i

Q: and the local maxima, local minima, and saddle points of the function, f(x, y) = x³ + 3xy + y³

A: Topic = Derivative

Q: 2x² + 3 Find f'(x) given that f(x)= x² - 5x+2 5) Find f'(x) given that f(x) = (2x³ + 2x² − 3)(3x³ -…

A: I am attaching image so that you understand each and every step.

Q: Express as a single logarithm and, if possible, simplify. 1 log b + 3 log c 2 1 log b +3 log c= 2…

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Q: A/ By using Linear equation solve the first order differential uation y' + sec(x)y= cos(x)

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Q: Q4/(A) Find the derivative of f(x, y) = xey + cosxy at the point (2,0) in the direction.

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Q: Q5) Find dw/dt at the given value foe the following functions 1) w = x² + y², x = cost, y = sint at…

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Q: Q6/(A)Evalute √2² £2ª ex² dxdy.

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: & Q6/(A)Evalute e*² dxdy. (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: In this question we have to find the Integration and partial derivative.

Q: * Parallel lines have the slope (m1x m2 )= -1 true O O False

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Q: dy = y2-y that passes through the indicated points. dx Find a solution of x (a) (0, 1) y = (b) (0,0)…

A: The solution is given in the next steps.

Q: 6 6 Suppose ff(x) dx = −4 and g(x) d -4 3 3 6 Evaluate (3 f(x) — 3 g(x)) dx. 3 Remember to include a…

A: Given that ∫36f(x)dx=-4   and ∫36g(x)dx=-3 we have to calculate , ∫363fx-3gxdx. To solve this…

Q: Q1/ im-1 2ܨ (s+1)(s-1)2

A: This question is based on inverse Laplace transform.

Q: f Cos 6 x dx 2 Cos ²3x

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

Q: Q5) Solve dx dx +2xy = 3 by using Euler's method to find the approximate solution up to X-2.9 when h…

A: The solution is given below