Q9- Find the turning points of the function f(x,y)=x^2+ 2xy and state whether the points are max, min or saddle points?

Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) A cos 2 B) e² CO (D) -sin 2

A: This question can be solved using the concept of partial derivatives.

Q: What integration technique can be used to integrate: (A) Integration Formulas (B) Integration By…

A: Option (d)

Q: 1. Set up the integral (but do not evaluate) to find the volume of the solid obtained by rotating…

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Q: test if (AB)¹ = B¹A¹ A = 4 1 0 2 L3 5. B = 14 0 2 - -3 1

A: To test if ABt=BtAt.A=410235, B=14-3021

Q: The area enclosed between the two curves x² = 2y and y² = 2x is rotated about the x- axis. Determine…

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Q: === =+ = ²x² 6 2x Find the arc length given: y = - on the interval [1,2]

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Q: dy dx + y = 2xy-ex

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Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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Q: 3. Use the given graphs to sketch the graph of f(x) + g(x). Explain your process. [A3] [C2] fox)…

A: We have to solve and draw the graph.

Q: √9-22 1. Sketch the region of integration first, then transform Finally, evaluate the resulting…

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Q: 4. 2x³y = y (g2 + 3z2)

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Q: dy Find the general solution of the differential equation: dt What is the integrating factor? µ(t):…

A: topic- differential equations

Q: 5. For the below ordinary differential equation with initial conditions, state the order and…

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Q: 10) Given the following exponential function f, where c> 1. f(x)=p(c)(x-r) + s In addition, p 0, r>0…

A: Solved below.

Q: Question 5 What is the amount of work done on a spring when it is compressed from its natural length…

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Q: {(† - ₹)}₁_^

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Q: :S- 8x + 1 √4x-3 dx. If we let the substitution "=√√4x-5, the resulting integral Given : becomes Ⓒ =…

A: The integration of the integral is (8x+1)sqrt(4x-3).

Q: 12. y = 3t 1+t³ X= 3t² 1+t³

A: We can find y' using chain rule as below.

Q: A region is bounded by the y=x2 and y=6x-x², Which of the following integrals would approximate the…

A: Option (a)

Q: √9-2³ x² + y² dy dr into a double integral in polar form. TITE f(x, y, z)dV, where f(x, y, z) = x²yz…

A: We can set up the triple integral.

Q: A region in the first quadrant is bounded by the curve >= 1+ sin²x, the coordinate axes and the line…

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Q: Write the equation in standard form. x 2 + y 2 - 8x - 4y + 12 = 0 ( x - 4) 2 + ( y + 2) 2 = 8 ( x…

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Q: π A region in the first quadrant is bounded by the curve y = 1+ sin²x, the coordinate axes and the…

A: Given problem:-

Q: Let K/L be ideal of quotient ring R/L. If K is prime ideal and contains L, then K/L is prime ideal.…

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Q: how would I find the domain of the vector function r(t)=cos(t)i+ln(t)j+1/(t-4)k?

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Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise fu…

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Q: 3. Find the inverse of the function: ƒ (x) = 4x² − 5

A: The answer is given below:

Q: A region is bounded by the y=x² and y=6x-x² Which of the following integrals would approximate the…

A: We can solve this as follows:

Q: a) x² x² + y² - 2² +22=1 ɔ) x² − y² + 2y + z² = 2 =) x² 4x − y² — z² = −3 d) x² - 4x − y² — z² = −4…

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Q: In the quadratic equation Ax² +BX+C =0, describe the roots when B²-4AC is zero. A The roots are…

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Q: The region in the first quadrant bounded by the graph of y=8-x32, the x-axis, and the y-axis is…

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Q: A biochemist is testing the effect of a new antibiotic on a particular mould growing in a petri…

A: We need to find time and rate of area increase. As per Bartleby's guidelines we can only solve 3…

Q: Q4: If f(x,y) = x²y + exy Siny Find 1) 2) (D = f), at po(1,0) in the direction of 0 = Po

A: Given problem:-

Q: Choose an item below and explain your selection. The direction of proj, u + vis 1. The same as u.…

A: When we write  projv→ u+v→    It means the components of vector u+v→ along the direction of v→…

Q: Find the exact value of the surface area generated by revolving the curve 1 + 1≤x≤2, about the…

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

A: Topic:- calculus

Q: 10. 2z + 3 2+2 11. 2z - i iz + 2

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Q: 2. Evaluate the integral. Do not use hyperbolic functions as the final answer. 1 =dx 2 √3x² - 4…

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Q: and A solid is generated by rotating a plane region that is bounded by the curves y = 2² = y about…

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Q: What integration technique can be used to integrate: Integration Formulas Trigonometric Substitution…

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Q: a. Find an equation of the tangent line at x = a b. Use a graphing utility to graph the curve and…

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Q: A man 5ft tall is walking along a straight line at a rate of 3ft/s towards a lamp post that is 15ft…

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Q: 4) Consider the following logarithmic equation: What is the solution to the equation? log4(x + 2) +…

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Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: 3 Safin designed and launched an app. One week after he launched the app, it had 8 400 users. Four…

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Q: Question Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 2), and (3,…

A: Given problem:- Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 2),…

Q: 13. The following functions are given: log3 X +3 4x-15 ● f(x) = g(x) = 2x+8 What is the value of f o…

A: To solve the following problem

Q: Use the theorems to evaluate the limit. lim x³ x → 2

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Q: Let f(x) = 2x³ - 3x² - 120x+7. a. Find all points on the graph of f(x) at which the tangent line is…

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Q: 11. Suppose a population grows according to a logistic model with initial population 300 and…

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