S sin?x cos³x dx i sin*x -sin*x + c i sin*x +sin°x + C O A B -sin'x -sin'x + d

Q: 4. Find the area of the region that lies under the graph of f over the given interval. a. f(x) = 2 -…

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Q: :Q: solve the following equations 2X-3Y+Z=-1 X+4Y+5Z=25 3x-4y+Z=2 x=8.7 y= 5.7 z= -1.3

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Q: Use the Trapezoidal rule with step size Ar = 1 to appoximate the integral f(x)dx where a table of…

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Q: DO NOT include spaces in between characters. * Find the value of at the point (0,1) given the curve…

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Q: Find y' if ey+y²=2x. yey – 2 y'= хе + 2у хе + 2у y'= ye – 2 хе*У + 2у y'= 2 – yey 2 – ye y'= хе*У +…

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Q: wo linearly independent solutions of the differential equation y"-4 y=0 are O y,=e** and y, = e 4x…

A: I am attaching image so that you understand each and every step.

Q: Evaluate triple integral f, SE Lx? - y?)dz dy dx.

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Q: Q2) Solve the D.E dy – (2x/1- y²)dx = %3D

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Q: integral is true or false: 3 dxdydz = 72. 0. 1 -3 Select one: Truo

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Q: 6.x'y 10. lim (х, у) — (0, о) 2.х* + y*

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Q: Consider the parametric curve defined by 1=3+5t and y=1+3 Over which values of doesthe curve has a…

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Q: Find the derivative of f(x) = x In(x) 1- In(x) O In(x) O1+ In(x) O In(x) /x

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Q: A particle is moving in space and its position at time t is given by r(t) 4(cos t)i+ 4(sin t)j+ /²k,…

A: Given problem:-

Q: Find the average value of the function f(x)=e" on the interval (0,4) Da 3725 Ob 490 OC 745 Od 186 25

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Q: Reduction of order can be used with 2x to find a second solution for the %D DE: 2x²y" – xy' - 2y =…

A: Given y1= 2x² is a solution of 2x²y''-xy'-2y=0....(i) So 2x²y1''-xy1'-2y1=0....(ii) Let y=…

Q: Cara tosses a pair of equally weighted coins 4000 times, and two heads appear 40 times. What is the…

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Q: Q2) Convert the polar functionr tan20 to cartesian.

A: Here we have to convert the polar function r=tan(2θ) to Cartesian.

Q: If f(x) = 2x + Ax?+ + Bx – 5, find the value of A when f(2) = -3 and f(-2) = -37 -5 -3

A: A=-15/4

Q: Which of the following yields the value 318? 3 (8х + 7у) dxdy 0 °0 (8x + 7y) dydx 0 °0 none of the…

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Q: 1 dx x[9+(ln 3x)" 8.

A: use simple integration method.

Q: Find the absolute extrema of the function f(x)=(x+1)*" in [-2,1], if there is any.

A: f(x)=x+123

Q: Which of the following is the general solution of the differential equation y" - 36 y=0 ? O…

A: y''-36y=0auxillary equation is given bym2-36=0(m+6)(m-6)=0m=-6,6m1=6 , m2=-6

Q: Q2) Convert the polar function r = tan20 to cartesian

A: We know that x = rcosθ, y=rsinθ Given: r=tan2θ

Q: sin x Let g(x) = 1 ot. Find the derivative d'(x). '2 1+t3 none of the choices cos X 1+ sin3x sin? x…

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Q: y ton(メツ) ン Q3 Find tanx 2 y-(1+x

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Q: dx Evaluate: x/9x2 + 4 None of the above V9x2 + 4 + 2 In 4 f (x) = +C © f(x) = -2ln V9x2 +4 + 2 + C…

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Q: 9x 4. J, 16+9x

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Q: Find the absolute extrema of the function f(x) =(x+1)* in [-2,1], if there is any.

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Q: Q2) Convert the polar function r tan20 to cartesian.

A: We have to convert polar equation into Cartesian equation

Q: A line with positive slope passing through (-1, 1) and intersects the parabola y = x² at the point P…

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Q: A man 6 ft tall is walking at the rate of 3 ft/sec toward a streetlight 20 ft high. At what rate (in…

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Q: dx Evaluate: xV x2 +4 (A None of the given choices ® n Vx2+4- 2 + C x² + 4 +2 Vx²+4-4 +C x² + 4 + 4…

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Q: In x2/25+ x² dx , we let x= 5sine. T True F False

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Q: 2 3) -2

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Q: 4 r4-y Evaluate triple integral , S S dz dy dx -2

A: We have to evaluate the triple integral  ∫-22∫x24∫04-ydz dy dx.

Q: 3. Given the functions f (x) = a? - 4, g (x) = Va+ 4, and h (a) = %3D %3D | x + 2 find the DOMAIN of…

A: Domain is the set of all values  for which the function is defined.

Q: 1+2 sec (Vx dx Į Va sin (/æ) tan (Væ) sin (/r sec (Vr and sec (Vx Hint: tan (yx =1. cos (Vx

A: Integration

Q: In x²/25+ x² dx , we let x=5sine. A True

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Q: Question 13 - [x²/25+ x²dx , we let x= 5sine. (T True F False

A: We have to find integration

Q: 3 Fin %3D tan (X?y) tanx 2.y=(1+x)

A: 1) ln(x2+y) =tan-1(x2y)  2)y=(1+x2)tan^(-1)(x).

Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: DO NOT include spaces in between characters. And, DO NOT include dy/dx in your answer. dy given x =…

A: Given - x=sin(x+y) Now we differentiate with respect to x  d/dx (x)=d/dx (sin(x+y))…

Q: Q5) Find volume of body bounded by z² + y² + x² = 9.

A: Explanation of the answer is as follows

Q: Q3) Evaluate triple integral , dz dy dx.

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Q: irvature and the radius of curvature at the stated poi r(t) = 6 cos(t)i +6 sin(t)j+ 7tk; t= 2 r the…

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Q: Q3) Find the Area bounded by the curves y? = x and x = 2y – y?.

A: The given curves are; y2=x & x=2y-y2   Now find the point of intersection between the curve y2=x…

Q: Solve the D.E dy -(2x /1-y2)dx = 0

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Q: n(A U B) = 25, n(A N B) = 5, and n(A) = 20 Find the value of y. A В 5 y Your answer

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Q: + c2e4x The auxiliary equation of a second-order homogeneous linear differential equation is m - 7m…

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Q: In solving the antiderivative of f(x) = 2- 3sin(x) by miscellaneous substitution, the substitution…

A: The function f(x)=12-3sin(x)