23. Given the triangular numbers 1, 3, 6, 10, 15,... Find the 7th and 8th term of the series. a. 26 and 24 b. 24 and 26 c. 28 and 36 d. 28 and 34

Q: Given the matrices A = - -4 0 4 [ 5 B. If my not possible possible -2 -2 - and B -2 0 189 0 3 3 2 A.…

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Q: What is the integral of f cos¹ (2t)dt? Ot+sin(4t) + sin(8t)] + C O None of the choices O cos² (2x)…

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Q: (x¹+y¹) dx - xy³ dy = 0 [Answer: y = 4x¹logx + Cx¹]

A: This question is based on Homogeneous differential equation.

Q: Evaluate: ffefdxdydz 0-1/1 O 01/12 O-1 S

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Q: Let z = √7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2.

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Q: √x +3 If f(x, y) = xy + 7 the domain of f(x, y). Select one: True False then the point (1, −7) is in

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Q: r(t) = (−2√√ť² – 4, 3 sin (4t), 3 ln (−5 – 2t)), then the domain of r is given by the interval…

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Q: f(x, y) = 75 + 8x+5 Find fx, fxy, and fxyx. 8x³ e-8y

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Q: f(x, y) = 6√x - y²e-³xy е a) b) + elw Find få and fy. Evaluate frzy (4, −1).

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Q: 2. If z = x+iy = (x, y) then (2,-3)(-2, 1) is A. (1,8) C. (-1,-8)

A: Given,             z = x + iy = (x,y) To find   (2,-3)(-2,1)

Q: What is the angle of inclination? x +₂y + 8 = 8=0

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Q: dz Evaluate: 5 10+2% 0 1 O Divergent 00 0-1 15

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Q: What is the area (in square

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Q: 2n Consider the series ₁ (-1)" (1 + 1)². Which of the following statements is true? n=1 The series…

A: A series ∑n=1∞ an is said to Converge Absolutely if the series ∑n=1∞ an converge and Conditionally…

Q: If f(x, y) = x cos y, then fry(0, 1) = ? Select one: O 1 -1 O None of them sin y

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Q: If f(x, y) = x³y + cos(x) then (fa, fy) = (3xy - sinx, x³). Select one: O True O False

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Q: Match the functions in Column A with their corresponding antiderivatives in Column B. Column A a.…

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Q: area bounded by a = √y, x = 0, and y = 3 with the axis of revolution at y-axis using horizontal…

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Q: Find the general solution of the following differential equation. y" + 4y + 8y = 0 NOTE: Use cy and…

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Q: lim x-x6-x O +∞ 00 ∞- O O 3 1 2 ||

A: topic - limits

Q: 2x² + 5x-1 x³ + x² 3 -dx x² – 2x

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Q: et dx √ (e² = d − 1)(e* + 2)

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Q: A police car is located 40 feet to the side of a straight road. A red car is driving along the road…

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Q: a. b. dx x+2x³ In S is Inx In 2x² + 1| + C X C √ √2x² + 1 + ₁ C. d. In|2x² + 1 1 + C In x + In|2x² +…

A: Given problem:-

Q: Consider the series Σ +∞ (-1)" n=1 n Which of the following statements is true? The series diverges…

A: Correct option (b)

Q: 5. (x² + y² + 1)dx - 2xydy = 0

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Q: Can you please show the working i do not understand.

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Q: If you can only answer one, please answer 99. The questions asks whether the series converges or…

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Q: if u=f(x,y), x=g(w) and y=h(w), using chain rule, what is ∂u/∂w?

A: Silution : Given that u = f(x,y)

Q: Question 40 The graph of y=2 is concave downward for all values of such that. 0 x 2 0x 0 < Previous

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Q: Question a) b) Let f(x, y) = 2√x - y²e-2xy Find fx and fy. Evaluate fxxy(4,-1). + NIA

A: Given :fx,y=2x-y2e-2xy+2y

Q: A heart-shaped graph in a 2D plane is defined by the equation (x² + y² - 1)³ = 4x²y³ Determine dy/dx…

A: See this solution in below

Q: dy Find using implicit differentiation. dx Hint: First clear the denominator to get 8x² + 6y =…

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: QB3) Verify fxy-fyx for the function f (x, y) = 4x (Iny) + 4y (Inx) + (²²4 2²

A: We have to prove fxy=fyx for the given function.

Q: a, b, and I are differentiable functions of the same variable what is the derivative of H ac b +…

A: To find the derivative of acb, here a,b and c are differentiable function of same variable. Let a,b…

Q: Vector A has a magnitude of 8.0 m, South and vector D has a magnitude of 10.0 m, 530 W of N. Find…

A: To find out the vector product.

Q: x - 1 = λχ y = 2 = λy z = -λz (x² + y² = z² = 0,

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Q: 1 Give the antiderivatives of X The antiderivatives of 1 2 are

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Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

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Q: Evaluate fx and fy at the given point. (If an answer is undefined, enter NONE.) f(x, y) = cos−1(xy),…

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Q: Work Problem for the question. Let You must provide a clear and detailed solution z = (y-2x)³. where…

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Q: After successfully passing the Technical Written Examinations, you're now at the PRC Main Office ta…

A: Given: there are 5 registrations specialist on different windows faciltaiting registrations, the…

Q: Work Problem for the question. Let where x = t = -1. You must provide a clear and detailed solution…

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Q: 01. |x2 - 1\dx = a. b. 2 C. 432 - 23 23 d. 틀-

A: This question can be solved using the concept of definite integrals and modulus function.

Q: Evaluate cosh² x dx }(sinh2n +2) + 0 +x + C O2e²x +4z + C 8 O None of the choices cosh(z)sinh(2)++C

A: We can solve this as follows:

Q: 1 -1 tan X x² +1 -dx

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Q: Use Leibniz's rule to find dy dx dy dx for y= 8x-1 √ (t4-5) dt.

A: Concept: Newton Leibniz Theorem : Newton Leibniz A formula for differentiating a definite integral…

Q: 11 1 2 (x-3)/3 -dx

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Q: uring Runge-Kutta Method of fourth order, salve dy + y + xy² = 0, $ (0) = 1 by taking h= 0.1 لا

A: Runge Kutta Method of fourth order :-dydx= f(x,y)   , yo = xoyn+1=yn+16(k1+2k2+2k3+k4)where k1= h…