2. Find the partial derivatives with respect to x and y for the function 3xy² f(x, y) = xy - x²

Q: Sketch the graph of the function. √√x O -4 f(x) = x 4 -2 (x - 1)2 if x > 2 y 4 2 y if x < -1 if -1 <…

A: Given query is to to find the graph and the limits which exists.

Q: A sum of $200 at 7% interest compounded continuously will grow to V(t) = 200e0.07 dollars in t…

A: A sum of $200 at 7% interest compounded continuously will grow to Vt=200e0.07t dollars in t years.…

Q: dz Find au du and dv when u = when u = |u= In 2, v=¯ π v = ln 2, In 2, v = 2 =(Simplify your…

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Q: _4. y=e*, y=0, x=-1, x = 1; about the x-axis

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Q: Find the arc-length parameterization for r(t) = (cos, sin).

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Q: -2 Which of the following properties are used when rewriting the expression 2a O same base product…

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Q: Evaluate the function f(x) at the given numbers (correct to six decimal places). f(x) = x² - 8x…

A: The function is given as , fx=x2-8xx2-x-56

Q: (b) g(x) = k, 3z²+16z+16 I+4 z I‡ -4. x = -4 k =

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Q: e20 sin 30 de

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Q: 45° 8 Q The height of a right triangle with base angle 45° and hypotenuse 8 is

A: Answer: The solution is given below:

Q: Find r(t) if r '(t) = t9 + 4t3 j-t5k and r(0) = j

A: Given query is to find indicated function.

Q: . Use Function Transformation to Sketch graph of the function below. f(x)=-3-√(2x - 4)

A: Given: fx=-3-2x-4 The parent function is of f(x): y=x

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Q: The distance of a particle from some fixed point is given by the following function. s(t)=t² +5t-4…

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Q: 8 A 3 B Note: Triangle may not be drawn to scale. Given the triangle above, answer the

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Q: Let f(x) = 2x³ - 6x² - 18x + 1. a. Find all points on the graph of f(x) at which the tangent line is…

A: Given query is to find the point s for indicated tangent condition.

Q: The differential equation -4e* cos(y) +4² -4e* sin(y) - 8yln(x) + 5y² Has solutions of form F(x, y)…

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Q: 17. y = x², y = 2x; about the y-axis Answer 8π/3 + y = 2x (2,4) y

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Q: Sketch a graph of the following hyperbola. Find the center, vertices, foci, and asymptote equations…

A: Given: x^2/ 36 - (y− 1)^2/4 =1

Q: The curvature of the helix r(t) = (a cos t) i + (a sin t)j + bt k (a,b20) is k=- 2,2 a+b What is the…

A: Given helix:- rt=acostiasintj+btk

Q: Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f…

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Q: How do we know that eª and In x are inverses of each other?

A: The given two functions are ex and lnx We have to prove ex and lnx are inverse of each other .

Q: Find the power series representation for the function and determine the radius of convergence R.…

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Q: . Given that y = 3x - 7 is tangent to y = f(x) at x = 2, find the tangent line to y = xf(x) at x =…

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Q: 98 x = 62° 29° NOTE: The triangle is NOT drawn to scale. Answer the following: Round your answer to…

A: We are required to find the value of x

Q: Given y = f(u) and u = g(x), find by using Leibniz's notation for the chain dy dy du dx du dx rule:…

A: Given: y=f(u) and u=g(x), find dydx by using Leibniz's notation for the chain rule:dydx=dydududx…

Q: 3. If f(x) = x² + 2x + 1, find f(x + h) where h is a variable.

A: fx=x2+2x+1

Q: The graph of g'(x), the derivative of a function g(x) is pictured below on the closed interval [-9,…

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Q: The magnitude R (on the Richter scale) of an earthquake of Intensity / is defined as (7) ► where Io…

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Q: (a) Use a graph of f(x) = = √2x² + 9x + 2 - √2x² + 2x + 1 to estimate the value of lim f(x) to one…

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Q: Use the shell method to find the volume of the solid generated by revolving the region bound by y =…

A: Let's find volume of solid generated by revolving about the y-axis.

Q: Given then lim h→0 is f (x) = O a b с d f(3+h)-f(3) h -1/3 -1/9 1 X, 3 9

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Q: Use differentials to estimate the amount of metal (in cm³) in a closed cylindrical can that is 22 cm…

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Q: If z = 8x² + y² and (x, y) changes from (1, 1) to (0.95, 0.9), compare the values of Az and dz. dz R…

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Q: Explain why the function is differentiable at the given point. f(x, y) = 7+ x In(xy-7), (4,2) The…

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Q: | dy F

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Q: Find the general solution of the differential equation: y'-1y = xy³. Use lower case c for the…

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Q: Assume that the function G(x) is measured in zots and x is measured in toots. What units would G'(x)…

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Q: 1) Suppose velocity, v(t), of an object at time t is given by this piecewise defined graph. Assume…

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Q: Determine if the sequence {an} converges or an = 5+ (0.4) diverges. Find the limit if the sequence…

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Q: Verify the following relations: a) n=1 1 Σ(n-1)³ n=2

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Q: Does the sequence {a} converge or diverge? Find the limit if the sequence is converge an = n 9⁰

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Q: (a) Estimate the area under the graph of the function f(x) 1 x+4 n = 10 subintervals and right…

A: Given function is f(x)=1x+4 from x=0 to x=4Then ⇒To find the area under the curve f(x) from x=a to…

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Q: K Use the given graph of the function to find the function information. (A) Intercepts (B) Vertex…

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Q: Solve for x using logs. Round your answer to four decimal places. X = Save for Later 10x+2 = 6e7-x

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Q: Solve the following system of nonlinear equations using either substitution or elimination. Write…

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Q: g) f(x)=√1-ecos(1-x²)

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Q: let f(x) be the function 12x^2-2x+7. Then the quotient (f(6+h)-f(6))/h can be simplified to ah+b…

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Q: 7. Find the point (a, b) on the graph of y = x³ - 3x² +4 where the tangent line is x - 3y = 1.…

A: given y=x3-3x2+4tangent line perpendicula to x-3y=1if two lines are perpendicular than there slopes…