1. Differentiate: y = √2 - 3x²

Q: A solid is contructed so that one side is the region between the lines x = a, x=b, the graph of y =…

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Q: TOPIC 4-5: L'Hôpital's Rule x²-25 x+∞5-4x-x² Q. #11 Please evaluate Lim a) Using L'Hôpital's Rule as…

A: L’hospital rule  limx— a f(x)/g(x)   = limx— a f’(x)/g’(x)   now find limit

Q: Find the volume of the region between the cylinder z= 3y and the xy-plane that is bounded by the…

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Q: Find the exact length of the curve y = br (ex :/) 1) + لے سلاے ахо

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Q: Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem. y" + gy…

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Q: Find all the first order partial derivatives for the following function. f(x,y,z)=x²y+y²z+xz² O A.…

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Q: Find all points (x, y) on the graph of y = x2 −6 with tangent lines passing through the point (3,…

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y=x and y=2-x…

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Q: Find all local extreme values of the given function and identify each as a local maximum, local…

A: Topic:- Application of derivetive

Q: Find the dimensions of a rectangle (in m) with area 2,197 m² whose perimeter is as small as…

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Q: Compute the line integral of the vector field F = (7y, −7x) over the circle x² + y² = 1 oriented…

A: Given: F=7y dx - 7x dyand Let  x= cos t,   y= sin t    ⇒   dx = -sin…

Q: The graph of a twice-differentiable function is shown in Which one of the following sets of…

A: Please see the below picture for detailed solution.

Q: Sketch a graph of a function f with the following properties. f' 0, for x 0, for -50 and f''>0, for…

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Q: Given f(x, y) = 2x² + 6xy³ + 4y5, find the following numerical values: f(3, 3) = 4. f₂(3, 3) =

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Q: 1. Determine an equation of the line tangent to the curve y = 2x² at the point with x-coordinate-2.

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Q: 12 1층 1 + du 6

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Q: Q16 A helicopter is rising straight up in the air. The distance from the ground t seconds after…

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Q: Obtain the general solution of the following differential equations 8. (y sin x + xy cos x)dx + (x…

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution to the…

Q: A rectangular storage container without a lid is to have a volume of 10 m³. The length of its base…

A: Given volume ( v ) = 10m3 let length = l width = w height = h

Q: Find f.  F"(x) = t2 - 4

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Q: A tank contains 500 gallons of salt-free water. A brine containing 0.25 lb of salt per gallon runs…

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Q: 4 16 16-y -!!!- Here is the region of integration of the integral a. dy dz dx b. dy dx dz c. dx dy…

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Q: The derivative of a function is given f'(z) = (2²-21-8)g(x) for some unspecified function g such…

A: The first derivative of a function is given by fx = x2-2x-8gx,   gx>0 To determine: The point…

Q: Consider the following vector function.. r(t) = (2√2t, e²t, e-2t) (a) Find the unit tangent and unit…

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Q: Complete the parametric equations of the line through the points (1,8,3) and (4,-6, (t) = 1 + 3t…

A: The parametric equation for the line through (x, y, z) and (a, b, c) is: (x, y, z)+t((a, b, c)-(x,…

Q: d Q10 Compute [3t²] (a) 3t² (b) 6t (c) 0 (d) 9t

A: We need to perform differentiation.

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3r sin(ry)…

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Q: An analyst find the data that the cost of 10 heaters is $ 2900 while the cost of 15 heaters is $…

A: Please see the below picture for detailed solution.

Q: As a graduation present Natalie received a sports car which she drives very fast but very smoothly.…

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Q: At which points on the curve y = 1 + 40x³ - 3x5 does the tangent line have the largest slope? (x, y)…

A: we need to find out the points on the given curve where the tangent line has largest slope.

Q: Find the area of the curve: y = 9-x² and the x-axis

A: We are authorized to answer one question at a time, so we are answering the first one. Please repost…

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A: Given:-  The solid obtained by rotating the region in the first quadrant bounded by the curv x = 0,…

Q: Use the following three identities to evaluate S sin sx cos tx = sin sx sin tx = cos sx cos tx = ·S=…

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Q: Find sin(t) and cos(t) for the values of t whose terminal points are shown on the unit circle in the…

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Q: 4. Point of Diminishing Returns Assume that an advertising campaign is launched for a new product…

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Q: Find the linearization L(x,y) of the function f(x,y)=²x cos (3y) at the points (0,0) and ¹ (0.7) The…

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Q: 113 Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: Two particles start at the origin on the s-axis at time t = 0 s and move along the s- axis. Their…

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Q: Determine h (x²) for the following function. h(x) = 4x x² - 4x + 5

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Q: Evaluate the limit sin 2x 8x lim x→0

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Q: Sketch-the-graphs.y = x² + 1, y = -x² + 2x + 51

A: we need to sketch the graphs of the function.

Q: Find the values of z, y and that correspond to the critical point of the function f(x, y) = 2z²-1z +…

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Q: Suppose that f is differentiable at 1 and f'(1) = 1 = f(1). Evaluate lim xf(x²+x-5)-16 22-4 (Hint:…

A: Given f is differentiable at 1 f'(1)=1=f(1) We are required to find limx→2x4fx2+x-5-16x2-4

Q: a tank contains 1000L of brine with 15kg of dissolved salt. pure water enters the tank at a rate of…

A: The answer is in step 2.

Q: Suppose a primal minimization problem and its dual maximization problem were solved by using the…

A: We have to find the solution of the maximization and minimization problems.

Q: Q17 Given P(q) = -2q² + 30q-25 (a) Find the profit from selling the 2nd unit. (b) Use marginal…

A: Given:- Pq=-2q2+30q-25

Q: why was x tan(t)?

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Q: Form a partial differential equation by eliminating the arbitrary functions from the relation z =…

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Q: Combine the sum of the two iterated integrals into a single iterated integral -3√2/2 xy dy dx √9-1²…

A: Convert into polar form

Q: For y = f(x) = 8x³, x = 3, and Ax=0.04 find a) Ay for the given x and Ax values, b) dy = f'(x)dx, c)…

A: We have, y=fx=8x3, x=3, and △x=0.04 To evaluate : (a) △y for given x and △x value (b) Expression for…