дz дz Suppose z is a function of r and y and tan(√x + y) = e²². Determine and 3x ду

Q: S dx x² √√x²-1²

A: Follow the procedure given below.

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Q: Find the inverse of the coefficient matrix and use it to solve the system. = 6 2x₁ + x₂ X₁ X1 + 2x₂…

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Q: Exercise (1-3): By Charpit method solve the following PDE (1): p²x+q²y=z

A: This is a problem related to partial differential method. Based on the general formula and concept…

Q: y' = X 2 h

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Q: S 10dz 4z3-4z²+5z

A: To evaluate the given integral:

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Q: f(x) = x³ +7x² - 5x

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Q: The graph of y=f(x) is shown. Draw the graph of y = -f(x). 17 Ex X 3

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1 x² dx √4-x²

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Q: (1 + x³) dy - x² y dx = 0, when x = 1, y = 2

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Q: Find Ans= dy dx for y = 3x + ex x² - 5

A: Using formula of d/dx(U/V)

Q: 3. Determine the limit graphically. Confirm algebraically. x - 1 lim x-1 - 1 1² - 3t+2 lim 1-2 1² 4…

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Q: dy Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dx…

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Q: 1. Evaluate the given integral Q. Q = $₁² [² (2² Your answer (x² - y) dy dx

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Q: Jack has 13 cards printed with the letters from the word “UNDERSTANDING,” so that “U” is in one…

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Q: Find the slope and the rate of change of the slope with respect to x when t = 90°. x = 2 cos (3t)-3…

A: This question can be solved using the concept of first and second order derivatives at t=90°

Q: Find the area of the region in the first quadrant that is enclosed by the coordinate axes and the…

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Q: Solve the following problems showing detailed solutions. Draw the complete figures for each…

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Q: An open-top rectangular box is being constructed to hold a volume of 400 in ³. The base of the box…

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Q: Find the second derivative of f(t) = [(1+)¹ +1]¹

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Q: Use Logarithmic Differentiation (as shown in lecture) to find the derivative of y = (4 + sin x)√T…

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Q: 0 Compute the integral: I alned

A: LetI=∫01xlnxdxApply integration by…

Q: 5/16 Find the enclosed area by the curve with equation y = 4-²,the X-axis and the lines x = -1 and x…

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Q: [x³√₁-x² x2

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Q: A lighthouse L is located on a small island 2 km from the nearest point A on a long straight…

A: A lighthouse L is located on a small island 2 km from the nearest point A on a long straight…

Q: 3√3 dx √3 x² √√x² +9 2

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Q: 1. Evaluate the given integral Q. -2 2y-2 -K² Q Jo 1 = (xy-1) dx dy

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Q: 6. Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3. Then the area…

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Q: 6. Find the intersection of the line I and the plane . 1:7=(4,-1,4) +t(5,-2,3) 2x+5y+z+2=0

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Q: 1. Evaluate the given integral Q. Q - CC² LL- (x - y) dx dy y²

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Q: Fermat's theorem states that if f has a relative extremum and if f'(x) exists, then f'(c) = 0.…

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Q: 7. Find the member of the curve whose slope at any point is 2e¹x and passes through the point (0, 1)

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Q: 'SC x x x

A: ∫cot2(x)csc3(x) dxWe know that cot2(x)=csc2(x)-1=∫csc3(x)(csc2(x)-1)dx=∫(csc5(x)-csc3(x))dxWe know…

Q: Find the derivative of the function at Po in the direction of u. 2x-y g(x,y) = 5xy +6 Po(1,-1),…

A: We need to find derivative of the function.

Q: 3t4 - 6t+ 3et Let f(t) = Then f'(t) =

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Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

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Q: 3. The vertical trapezoid plate shown is below is the end plate of a trough full of water. Write but…

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Q: 3) (2) 2 3 元16 2 " 11元 6 57元 6 3 2

A: We have to plot a given point in the graph.

Q: The entire graph of the function h is shown in the figure below. Write the domain and range of h as…

A: The domain of a function  f(x) is the set of all possible values of x for which f is  defined. The…

Q: Given cost and price (demand) functions C(q) = 150q + 47,100 and p(q) = -2q +890, What price must…

A: This question is related to cost and price functions, we will solve it using given information.

Q: exey (2xe + )dx + ( ) dy - ex ر ول

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Determine the indefinite integral. 25 dx x In 7x 25 S= Sx157x x In 7x dx =

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Q: x³ - 125 lim x-5 x - 5

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Q: Evaluate the definite integral. 16 (10y√y +9√y) dy 16 jo (10y√y +9√y) dy = (Simplify your answer.) 4

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Q: Find dy/dx and d2y/dx2 of x= t + 1/t, y= t + 1

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Q: 1. f(t) = (t5+t) (t³ - 4t+1) 2. g(x) = (+1)(3x - 1) 3. h(x)=¹

A: Topic:- function

Q: Problem: 1. Find the area bounded by the curve y = x² and the line y = 6.

A: Given query is to find the area bounded by the curve.

Q: The general solution of y” + 4y = 3 sin 2x

A: Given differential equation, y"+4y=3sin2x...(i) So, corresponding homogeneous equation,…