2 Find the curvature of the parabola given by Y = X = = x ² a+ x=2 Sketch the circle of curvature at (2,1) and find its center and radius

Q: 2. Find the anti-derivative of the function f(x) = e* sin (^te^)

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Q: Two cars approach an intersection at right angles, one traveling north at 60 km/h and the other…

A: We have to find the rate at which distance between the cars is changing.

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: r=135 in h=168 in Rate of increase of radius=1.2 in/sec Rate of decrease of height=-2.8 in/sec

Q: Compare the functions f(x) = x³ and g(x) = ex by graphing both functions in several viewing…

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Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y₁ x = s + 2t - u, y = stu²…

A: z=x4+x2y, x=s+2t-u, y=stu2 given s=1, t=3, u=5

Q: Suppose that the marginal revenue for firefighting protective clothes is MR = 258 - cost is MC =…

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Q: Let r₁(t) = (-7, -6, -3) + t(0, 2, -3) and r₂(s) = (5, -10,-5) + s(3, 0, -2). Find the point of…

A: We want to find the point of intersection of the given two lines.

Q: that the indicated family of functions is a solution of the given differential equation. Assume an…

A: The given differential equation is;  d2y/dx2 - 6dy/dx + 9y=0

Q: Solve the given differential equation by separation of variables. dy xy + 7x-y-7 dx xy - 2x + 8y -…

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Q: Evaluate. Use reduced fractions instead of decimals in your answer. 8x e +3 ¡(² 4x e dx = + C

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Q: Use polar coordinates to find the volume of the solid below the paraboloid z = 50 - 2x² and above…

A: Here we use the polar coordinates;

Q: How do I use the chain rule to find the derivative of (y=(cosx+2sinx)8)? I know (cosx=1) and…

A: Chain Rule of differentiation: If y= f(u) and u=g(x) , then y=f(g(x)) , so then                 dydx…

Q: 7. Sketch the region and then use the disk/washer method to set up an integral to find the volume of…

A: To sketch the region and then by using the disk/washer method to set up an integral  to find the…

Q: Find the arc length of y = (*2²)* + over [1,4]. 2(x+2)² (Use symbolic notation and fractions where…

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Q: Hi I need help on solving this problem for my calculus: Evaluate the limit: lim x -> (3pi)/(2)…

A: limx→3π2sin2x+6sinx+5sin2x-1

Q: дz дz Use the chain rule to find and მs at z = ln(3x + 4y), x = s sin(t), y = t cos(s) дz as дz at…

A: z=ln3x+4y , x=s sint , y=t coss

Q: 5. The golf ball manufacturer, Pro-T, has developed a profit model that depends on the number x of…

A: To find : maximum profit and values of x and y to maximize it.

Q: 2. Consider the function: a) Determine the derivative. y = 2sinx b) Calculate the exact value of x…

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Q: 3. Determine the absolute extreme values for the function Y=3sinx + 4cosx on the interval [0,27]

A: y = 3sin x + 4cos x ,on the interval [0, 2pi]

Q: Answer: f" (x)= 2x (x² In² (2)-2x In (2)+2) X³

A: f''(x) =[2x(x2ln2(2)-2xln(2)+2]/x3 Find the value of the function at x=2.

Q: Evaluate the double integral changing to polar coordinates. ¹/1₁ (² (2x - y) dA, where R is the…

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Q: Find the first partial derivatives of the function. Əw ди Əw Əv 11 W = Need Help? ev u+v5 Read It

A: Given

Q: Use the graph of the function f shown to the right to find f(-4), f(-3), and f(-2). f(-4)= f(-3) =…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) [ sin(10x) sin(cos(10x))…

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Q: Consider the graph of the function f. f(x) -10 -5 Yet 5 5 - 10 5 Use interval notation to determine…

A: As per our company guidelines we are supposed to solve first three subparts only please repost other…

Q: If the velocity of a moving object is t 2 1² v (t) = 20 2 in meters per second, then what is its…

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Q: 1. The graph of f(x) is shown to the right. On the same grid, draw a sketch of f'(x). VA Explain,…

A: Given: Aim:  To draw the sketch of f'(x).

Q: (a) Show that (b) Solve the equation -1 cos(2 tan ¹x): = (d) Find the general solution to cos 7x…

A: Note : As per our Guidelines , we can solve first part as your all parts not too small . Please…

Q: Construct a problem where you have to find the inflection point that is equal to 1/2.

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Q: Evaluate the integral. 6 (x + 1)(x² + 16) 6 (x + 1)(x² +16) dx -dx=

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Q: To solve the following problem, use the Limit definition of derivative. a) For the function f(x) =…

A: To solve the following problem, by using the limit definition  of derivative. (a) For the function…

Q: 2. Find F'(x) if F(x) =tan(3x² + 2x). Solution: U= du dx 11 dy du dy dx 11

A: As per our company guidelines we are supposed to solve first question in different questions so…

Q: Suppose f(x) = 4x + 1. Determine, in a simplified form, each of the following: (a) f(a) = (b)…

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Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1 and a z-intercept of 5.…

A: The x-intercept is 4 The y-intercept is (-1) The z-intercept is 5 So they can be written in ordered…

Q: f(t) = t sin(at) 14. f(t) nat

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Q: If the slope of the tangent line to the graph of www y=f(x) at x=a is m (a) = 2a-3, and f(1)=5, then…

A: We have,   m(a) = 2a -3     f(1) = 5

Q: a. AOR: y = 0 b. AOR: x=0 c. AOR : x = 2

A: Since you posted multiple subparts, I need to solve only first three subparts.

Q: +(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation.…

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Q: 2. Locate all local extrema and saddle point(s) of f(x, y) = xe cosy for (x, y) = (-T, T) x (-π, π).

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Q: Find an equation of the line tangent to graph of F(x) x² + 1 x²_4 2 (3,2). write the equation in the…

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Q: Find all values of m so that the function  y = xm  is a solution of the given differential equation.…

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Q: Evaluate the definite integral. 7 7 4 X X-5 X X-5 dx = dx

A: To evaluate the following definite integral. ∫47xx-5 dx

Q: 29 / 36 determine the derivative function (for). 9. Let f be the R²R function defined by f(x, y) =…

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Q: (3) Find the equation of the line tangent to f(x)=√x atx=4

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Q: A spherical balloon is being inflated Find the rate at which its volume V is changing with respect…

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Q: Write the following expression as a single definite integral of the form f(x) dx. [²_1(x) dx + [³1x)…

A: Given expression is ∫-22fxdx+∫25fxdx-∫-2-1fxdx

Q: Set up an integral representing the area A of the region enclosed by the given curves. y = 5x, y =…

A: The area between the curves y=f(x) and y=g(x) from x=a to x=b is given by the integral…

Q: Answer with "true or false". In addition, if the answer is wrong, correct the statement.     If…

A: Given f(x)=xex, then we have to check f'(x)=x2ex that whether this statement is true of false.

Q: 7. Given = [-4,4,4] and ✓ = [-5,6, 2] find a. 2ū + 4v b. c. u x d. lul V V

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Q: Find the cosine of the angle between the vectors (1, 1, 1) and (8, -7, 12). (Use symbolic notation…

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