lim (x,y) → (0,1) In (x4 + 2 y ² - 1) e 2x² + y² - 2

Q: x²-2xy+5y²+1 lim (x,y)→(0,0) 3x²+4y²+2

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Q: Let f(x) = {ax² (2x + b differentiable (a) 1 at x = 1. x ≤ 1 x>1 (b)-1 . Find a so that f is (c) 2…

A: Here is the solution:

Q: 2x3y3 + cos(x. y) lim (x.y)-(0,0) (x + 1) 2 sin T +y

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Q: Derive that (x + y)(x' + z)(y + z) = (x + y)(x' + z) by using boolean algebra.

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: Use Picard's theorem, find the largest interval for which the IVP (x – 8)(x – 1) -y'%3D (x-6)(* +1)…

A: To find the largest interval on which existence and uniqueness guarantees a unique solution. For…

Q: Find the domain of analyticity for g(z) = -y3 – 3x²y + 3y + i(x³ + 3xy² - 3x).

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Q: (x²y3 - 5y2) lim (x, y) →(4, 2)

A: Given that, There is an expression of limit is following, lim(x, y)→(4, 2)(x2y3-5y2) We have to find…

Q: A function f(1) is given by f(1) = h + ab' and has the properties: • f(t) has a horizontal asymptote…

A: NOTE: Refresh your page if you can't see any equations. . the exponential function is given by here…

Q: Let P(x)—-x*+2х*-бх'-5х—1 and D(x)—x+1 Determine the remainder when P(x) is divided by D(x)

A: P(x)=-x23+2x12-6x7-5x4-1D(x)=x+1x+1=0x=-1

Q: -2? + 15z - 27 f(z) = 3z2 + 7z + 6 C, I= 3 What value of C would make f(x) continuous at z = 3?

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Q: Consider the rational function f(x)=8x/x−5. a)As x→−∞, f(x)→ b)As x→∞, f(x)→

A: We have to find limit

Q: tan(1 – x) 2 limx→1 2x +x – 3

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Q: If g (x) = x* - 2x3 – 7x² + 8x + 16,find g (-1), g (-2),g (2),g (3)

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Sa cos(r) dr = ,2 %3D 1 sin(r³) +c cos(r³) + c -1 - sin(r*) + c 3 cos(r³) + c 3 1/3

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Q: Suppose f(x,y) = sin-' (6 – 2x2 – y²) and g(x,y) = 4x2 – y2. Determine the continuity of the…

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Q: Let f(x) = {x²ca-1), Sx²e2cx-1), lacos(2x - 2) + bx? x>1 f(x) will be differentiable at x = 1, if…

A: We have to solve given problem:

Q: 40 Find x² + 1 lim tan (x, y)→ (0,1) x²+ (y – 1)² ] |

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Q: 3. h(x) = -2x³ + 5x² + 4x° – 3x + 12x? - 4 !! f (x) f(x) →_ as x → -00 as x → +00

A: We have to find the limit of the given function.

Q: limn→∞ √n = ∞

A: Given :limn→∞ n

Q: an =  (8n − 2)! (8n + 1)!   a1 =   a2 =   a3 =   a4 =   a5 =     lim n→∞ an =

A: Consider the given nth term an=8n-2!8n-1! Since, 8n-1!=8n-1 8n-2! So, an=8n-2!8n-1!=8n-2!8n-1…

Q: If z=xtiy where x and y are real, find the real and imaginary parts of:- Z-1 Z+1 ピージ (x+アア 2.xy…

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Q: lim (sgn(x² – 1) + [x + 3]) = ? X→-- 2

A: see below the answer

Q: Which table is a probability distribution table? X 1 P 0.4 X 1 P 0.4 X 1 P-0.2 X 1 P 0.2 2 0.15 2…

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Q: Find f(x) and g(x) such that h(x) = (f • g)(x) a. h(x) = V5x – 2 b. h(x) = 19x² – 4| c. h(x) = tan…

A: Authoring guidelines: As per the authoring guidelines we can solve only the first three parts of…

Q: Let f(x) = g(x) (x - 1)(x - 2)(x – 3)°(x – 4)³, where g(x) = x + bx² + cx + d. If f(x) is…

A: Use the following formulae, to obtain the required result. duv=udv+vdudu+v=du+dvddxxn=nxn-1

Q: (a) (b) x + y f(x, y) = √√x+y f(x, y) = sin (x+y) √√²-1

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Q: 85 2 1 r³)(1 x2 O A. (3x? – 2+ 3 - O B. 85 2 1 (3x2 – 2+ -x3)(x+ 3 · (1 – →)(x³ – 2æ + 17x3) 85 2 1…

A: Given query is to find the derivative using product rule.

Q: S²2 Sex+257 ² cos(3y² – 1³) dydx 2

A: The given integral is:∫-22∫x+22x+2 cos3y2-y3 dy dx

Q: The antiderivative of the function f (x) = 3(x³ – 1)² (3x²) is F (x) O ( - 1)° (9x²) 3(x³ – 1) (x³ –…

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Q: 2t – 2 t2- 1, Let r(t) = - î - tan (t) ĵ+ In(2t) k. %3D (a) Determine the domain of r. (b) Compute…

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