1 g(x)= {x-1 if x > 0 |x² −1 if x≤0

Q: Find y = (2x²² -6) ⁹ dy اده

A: We can find the derivative as below.

Q: The domain of the function f(x) = √3x + 23 consists of one or more of the following intervals: (-∞,…

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Q: Cut out squares (of the same size) from the four corners of a square cardboard of given side length…

A: The side of the square = L  let the length of the square = x,

Q: 1. Sketch the graph of r=1-cos in polar coordinates. [3 marks]

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Q: 5. An object has a constant acceleration of 10 ft/sec², an initial velocity of -20 ft/sec, and an…

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Q: Find the function f if. Vf-(3a²y + y², a² + 2xy), Vf dr with and without the Fundamental Theorem of…

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Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A: To find the critical points of the following function. By using the Second Derivative Test to…

Q: Find the absolute maximum and minimum values of the following function on the given region R.…

A: To find the absolute maximum and minimum.

Q: e 1 Determine the equation of the tangent line y=x=2( at x

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Q: A ball is thrown into the air and it's position is given h(t)=-4.9t + 60t + 5cm. Find the hight at…

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Q: Find the function whose tangent line has the slope e for each value of x and whose graph passes…

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Q: cook Use the power series f(x) = In (1-x) = - Σ for -15 x <1, to find the power series…

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Q: I = √x f(x, y) dy dx-

A: ∫01∫0xf(x,y)dydx

Q: H J A: x = B: x= C: x = D: x= E: x= F: x= G: x= H: x= Identify the points of the circle above. 1: x=…

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

Q: Find the derivative of f(x) = (2x+1)³(3x - 1)³. Show all your work and factor the result completely

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Q: integral

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Q: 3 Solve the following ODES by Inverse Operator method 2 • (B³² +1) y = cos x 11

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Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

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Q: Find the volume of the solid generated by revolving the region bounded by the curve y = In x, the…

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Q: Show that y=sec^2x and y=tan^2x have the same derivative. What can you say about y=sec^2x-cot^2x?

A: Given y=sec²x and y=tan²x Now derivative dy/dx=d/dx( sec²x) =d/dx(1+tan²x) dy/dx= 2tanx sec²x   Now…

Q: Determine the remaining sides and angles of the triangle ABC. What is the measure of angle B? 0° B…

A: This is a problem related to sine cosine rule of trigonometry. Please follow the procedure given…

Q: Average Cost Jesaki Water Sports incurs the following costs in producing a water ski vests in one…

A: Here we have to use the concept of derivatives

Q: The radius of a right circular cylinder is measured to be 15cm and its height is measured to be…

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Q: Find the derivative of the following function. f(x) = sinh 16x

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Q: Find the solution of the given initial value problem: y (4) + 2y"+y = 3t+6; y(0) = y'(0) = 0, y" (0)…

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Q: Write an expression for the polynomial of least possible degree graphed below. Leave your answ…

A: The solution is given below

Q: If y'=x³+y2, where y=1 when x=0, find a degree 3 polynomial that best fits the solution using Taylor…

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Q: me Determine the equation of t e 00 te tragen ܘܪܐܐܝ tangent line to y 3- 22+1 at 2:

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Q: 1. Simplify fully. Write each expression with positive exponents only: 6a -b √√-270x (2a 5-32 √9(x)⁰…

A: Follow the procedure given below.

Q: Find three positive integers x, y, and z that satisfy the given conditions. The sum is 33, and the…

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: Complete the statement. If a function f has an inverse and f(x) = -1, then f (-1)=_ If a function f…

A: The function f has an inverse function and fπ=-1

Q: Use the power series f(x) = In (1-x) = -for-1sx<1, to find the power series representation for the…

A: The power series fx=ln1-x=-∑k=1∞xkk, for -1≤x&lt;1 we have to find the power series for px=9x8ln1-x

Q: 72. Function f(x) = cos 2x, π 0<< 2 Real Number a = 1

A: Given: fx=cos2x 0≤x≤π2

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: Find the length of the curve. 1 10x3' y 6 + 1 ≤ x ≤4

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: Given plane is passing through the points (4,2,1) and (4,1,-6). Let A,B C are direction ratio of…

Q: Vf(1, 3) =

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Q: 3. A science project studying catapults sent a projectile into the air with an initial velocity of…

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Q: Use the substitution u=x2+4 to evaluate the indefinite integral below. 2x(x2+4)8

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Q: lim x→−6+ e²x x +6

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Q: Find the absolute extreme values of the function on the interval. F(x)= == 3 21 0.5≤x≤2 OA. absolute…

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Q: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

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Q: 2. Determine whether or not the series converges. State clearly the test you use, and show all…

A: We have to check the convergence

Q: 3. f sin√tdt

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Q: F(x, y, z) = -k At (-2,-2, -2) the vector is At (-2,-2, 2) the vector is At (-2, 2, -2) the vector…

A: Given vector field F(x,y,z)=-k Here k is constant

Q: -y(2x+y) x(x+2y) - y'=-

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Q: 3 5 58 a. A-¹BT Given A = and B = -2 -5 3 7 find

A: Solution is given below:

Q: Use long division to find the slant asymptote f(x)=2x2+7/x

A: