Q: hav is that not the function defined by ху f(x, y) √x² + y² if differentiable at (x, y) + (0;0) if…
A: We have to show that f(x,y) is not differentiable at (0,0)
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A: Here is the solution:
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A: We have to substitute z=√(4-x^2)
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A: Given problem:-
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Q: A) 0 B) 3 (C) 2 (D) 4 E 5 F) 1 Use polynomial long division to write 2x² + x³ 3x² + 4x-9 x² + x =…
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Q: E) Evaluate the triple integral on the left in each of the following: (a) ff₁dz dx dy = 1 "dz dy dx…
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Q: B. For the figure shown below, find the sum of the areas of all the semicircles. 47
A: I am attaching image so that you understand each and every step. Answer is 227π512 square unit
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A: I am attaching image so that you understand each and every step.
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Q: your cimal places. Radioactive substance X starts with a mass of 20 g. The half-life of the…
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A: We can solve this as follows:
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Q: he sum of one number and four times the second is 24. Their product ust be as large as possible.…
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Q: 27) 5 1 dx √x²- A) in (x+2+25+C In 5+X In +C 10 5-x nt B) +C X+5 D) (x+12-25374c In +C
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Q: 18 1510 18 50 Change the Cartesian integral - Change the Cartesian integral into an equivalent polar…
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Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…
A: On solving this we will get
Q: Find the average of the given function on the given interval. (a) y = cos x, [0, 3π/2] (b) y = x² +…
A: a) y=cos x, 0, 3π2b) y=x2+x+1, 0,1
Q: 10) Using the First Derivative Test, what are the local extrema for the function 5(x)==x²+10 x³…
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Q: 2log, x-log, y+log, z
A: Follow the procedure given below.
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Q: y = x² and x² = y
A: Area of the bounded region is
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- -π∫π ecosx dx to the integral value; a) With the Trapezoid Rule. b) Make an approximation with Simpson's Rule.Use integration by parts to evaluate the integral. ∫0π/3 5exsinx dx type an exact answerFast pls solve this question correctly in 5 min pls I will give u like for sure Mnty Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x^2+y^2=144 and x^2-12x+y^2=0
- Q. Evaluate using Cauchy’s integral formula. (Image attached)1. a)Evaluate a double integral by converting from rectangular coordinates. ∫∫R(x + y) dA where , R = {(x, y)| 1 ≤ x^2 + y^2 ≤ 4, x ≤ 0} b) Please solve no. 5) from the image attached. Thanks. Also, if you face problem understanding part a, you can look at no. 4) of the image. Thanks again.Find the general indefinite integral ∫ v(v2 + 2)2 dv *please use handwriting not typing, I understand it better that way. thank you*
- Green’s Theorem for line integrals Use either form of Green’sTheorem to evaluate the following line integral.write definite integral which computes the area of a surface of revolution from rotating y=(1/3)x^(3/2) on {0,8} around the x-axis. do not integrate it, just write it.Evaluate the definite integral D=∫π/20sin(2t)dt. NOTE: Use exact values only. Do not provide a decimal approximation for your answer.
- Identitfy the technique used in solving the problem. i.e. Trig sub, u-sub, by parts etc integral sign: e-2xcos(x) dxShow how to approximate the required work by a Riemannsum. Then express the work as an integral and evaluate it.9. A heavy rope, 50 ft long, weighs 0 . 5 lb / ft ?and hangs overthe edge of a building 120 ft higha) How much work is done in pulling the rope to the top ofthe building?(b) How much work is done in pulling half the rope to thetop of the building?Show how to approximate the required work by a Riemannsum. Then express the work as an integral and evaluate it. An aquarium 2 m long, 1 m wide, and 1 m deep is full ofwater. Find the work needed to pump half of the water outof the aquarium. (Use the fact that the density of water is 1000kg/m3.)