1- Let n and r be positive integers such that r≤n. Then (a) Pn=nx pn-1 (c) P = pn n-1 (b) P = P-1 (d) Pnx P₁ r-1

Q: Find dy/dx if y=2 – x^2.

A: Given query is to find the derivative of the expression.

Q: Using the Simpson's rule, the approximated value for the integral: f, dx, is equal to -3 0 6 None of…

A: A detailed solution is given below.

Q: Evaluate the given integral by changing to polar coordinates. sin(x² + y²) da, where R is the region…

A: Given that,

Q: 4. xy = COS (²) + +1

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Q: 5.2 Consider the curve that passes through the point (0,10) and is such that the slope of the…

A: We have to find the curve that satisfies the given conditions of the problem.

Q: 2. Evaluate the definite integral|z- 3| dr. (a) (b) (c) (d) 25 2 25 2 29 29

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Q: 5. The sequence of partial sums of the equation Σ (a)3/2 (b) 3/4 n=1 3n-1 (c) 1/3 (d) -1/3

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Q: Q1.B. if k-1 is an eigen value of (₁2). find one corresponding eigen vector?

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Q: find the explicit solution of y' +xy = x√ y

A: This is a basic differential equation problem

Q: Evaluate the integral. 11 sec 40 tan ²0 do 11 sec 40 tan ²0 d0 =

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Q: Given that f(z) = (z+ 2)(z²z+4) Find f(1 - 2i)

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Q: 77. an = (In 3 In 2) + (ln 4 − ln 3) + (ln 5 − ln 4) + - - + (In (n − 1) - ln (n − 2)) + (lnn − ln(n…

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Q: Find the net signed area of ƒ (x) = x - 2 over the interval [0, 6], illustrated in the following…

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Q: (b) Using implicit differentiation Find the derivative of 1. y³ + 3x²y = 13 with respect to x and…

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Q: Question 1. A critical point of the function g(x, y) = ey + 3x²y-y is (0,0). Use the Second…

A: See this solution in below

Q: 11. Find the angle between the planes: 4y + 3z = -12 and 3x +2y + 6z = 6.

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Q: Refer to functions s and t. Find the indicated function and write the domain in interval notation.…

A: Given sx=x-3x2-36 and tx=x-63-xWe need to find stx and its domain.

Q: Q2.B. A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is…

A: Given that, A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another…

Q: Lets a real constant such that s ≥ 0 in the process of calculating = 1,500 3.1 di you get: O a) I =…

A: s real constant such that s≥0I=∫1+∞x-3.x-sdx

Q: Find the coordinates of the points of inflection for the function. 14) f(x) = 7e-x²

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Q: ४ = (y3/2/3) - y¹/2 from y = 1 to y = 9

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Q: In the attached figure are represented the continuous functions g: R → R and h: R → R 9 h If it is…

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Q: Determine if the series. HE 10 n² 4n+3 74 converges or diverges. If the series converges, give its…

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Q: Refer to functions p and q. Evaluate (qop)(x) and write the domain in interval notation. Write your…

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Q: Write an equation for a rational function with: Vertical asymptotes at x = 3 and x = -4 x intercepts…

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Q: Given that F(x) = a) F'(x) bl 5'(4) 2 1 1 + 2 dt.Using the 2nd Fundamental Theorem of Calculus, find

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Q: Find the derivative of the following function. 8x e y= In 4x y'=

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Q: 2) Find the radian measure of angle 0 in the figure below. 22.5. a) O 2.25 radians b) O 4.5 radians…

A: we know that arc 2πR =2π radians

Q: Find the largest open interval where the function is changing as requested. 24) Increasing…

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Q: дz If x² sin(2y - 5z) = 1 + y cos(6zx) defines z implicitly as a function of x and y, find [Show…

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Q: Determine where the function discontinuous. [-(x+2)² +1→x≤-2 f(x)=x+1→-2≤x≤3 [(x-3)² −1→x>3 Using…

A: the given function,  f(x)=-x+22+1,x≤-2x+1,-2≤x≤3x-32-1,x>3

Q: 1215 + 1² + t³ - tdt

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Q: If u = 4j – 2k and v = 2ỉ − j + 7k, find ú.v. Select one: O √110 O-18 O √18 O 18

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Q: 1. Find the area bounded by r = cos 0 for -π/2 ≤ 0 ≤π/2. 2. Find the length of the r(t)= , 1≤t≤ 5 3.…

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Q: Q1\A: Find the value of K in the following linear system which is make the solution failure Kx+3y=6…

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Q: Q1): Determine the general solution of the O.D.E: (1-x) y'-y²=0

A: The given differential equation is:  1-xy'-y2=0   As we know that; The Power Rule: ∫xndx=xn+1n+1+C ;…

Q: A particle moves in the yz-plane along the curve represented by the vector-valued function r(t) = (4…

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Q: A region bounded by f(x) = 3 − x, y = 1, and x = 0 is shown below. Find the volume of the solid…

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Q: a-limx-4(2)

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Q: where a = and b = 16 10% f(x) dx = f* f(x) 10 24 [*1 (2) dz - f(2) f(x) dx

A: To find the value of a and b.

Q: B: Solve the following integrations: fx³e-2x¹ dx b-S. -dx x³ +10 c-f 3sec³x. tanx dx arks

A: a) ∫x3e-2x4dx Let x4=t Then, 4x3dx=dtOr, x3dx=dt4 By substitution,…

Q: P/ find the slope and y-interceft of the line. 8x+59=20

A: In this question we have to find the slope and y-intercept of the line.

Q: Find the area between f(x)=x² - 16 and the x-axis from x = 0 to x = 7. The area is square units.…

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Q: Consider the integral 11 [™ (22² + 2x + 1) da (a) Find the Riemann sum for this integral using right…

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Q: (2) Find an expression for the area under the graph of f as a limit. Do NOT evaluate the limit. g(x)…

A: given :   g(x)=x+lnx

Q: Find the area between f(x)=x²-12 and the x-axis from x = 0 and x = 2. The area is square units. ...

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Q: 11. Integral sin³ R cos R dR

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Q: Consider f(x)=x*. Find the first derivative, f'(x).

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Q: 10. Determine the point on the line x + 2y = 2 that is closest to (0, 0). Draw a sketch.

A: point which is closest to origin

Q: Find the equation of the tangent to the function y = cos(2x) at the point where x = л/4.

A: equation of a tangent line