Prove the following identities. cos( - ) sin x/2

Q: The Distance from P( 5,3) to Q(2,-1) is

A: Compute the distance between x1, y1, x2, y2:  x2-x12+y2-y12The distance between 5, 3 and 2, -1 is =2...

Q: Find the area of the shaded region. y 20 (1, 7e) 15 y = 7e* 10 5 y=7xe* X -1.0 -0.5 0.5 1.0 1.5 2.0

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Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 400e -x2 - 5y2 - 722 where T is measur...

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Q: Given: cos a= -, sin B=, aand Bare second-quadrant angles; find cos(a - B) 117/125 3/5 4/5

A: We have to find the cosα-β Given    cos (α)=-2425 , sinβ=35

Q: ds using the trapezoidal rule and Simpson's rule. Determine Evaluate The value of -ds is (Round to f...

A: Topic:-  integration   

Q: (d) dx a + x (e) 1 da J (a + x)2

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Q: Refer to the figure and find the volume V generated by rotating the given region about the specified...

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Q: Question 1: The lateral surface of a (right) cone is given by LA = TrVh² + r2 where h is the height ...

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Q: Given the function f'(x) = x(xxt 4)(x – 5)³, what conclusion can be drawn directly from the sign cha...

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Q: A discrete random variable X has the following probability distribution: 3 4. 1 2 P(X) y 9 1. Find y...

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Q: Evaluate the iterated integral | (a+ 2y) dyda. Give your answer correct to 2 decimal places.

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Q: (2+ In²x) dx J x(1 - In x)

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Q: Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downward? O...

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Q: Show that ri =1+i, r2 = 1-i is a solution of (3+ i)x + (1+ i)x2 = 4 +4i %3D

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Q: +oo n+1 n=1 Determine whether the sequence converges, and if so find its limit. If the sequence dive...

A: an =nn+1a1 = 11+1 a1 =12a2 = 22+1 a2 =23a3 = 33+1 a3 =34a4 = 44+1 a4 =45a5 = 55+1 a5 =56

Q: 16 Evaluate the integral: x² /x² + 49 (A) Which trig substitution is correct for this integral? Ox =...

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Q: Determine the global extreme values of the function f(r, y) = 4x³ + 4x²y + 2y², x,y > 0, x + y < 1

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Q: tanh 2x In (cosh 2x)dx

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Q: y2)dx = xdy when X2 ; Y- 3

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Q: Find the critical points c that correspond to local minima. (Use symbolic notation and fractions whe...

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Q: we might learn in a physics class that the air pressure can be found as a function of altitude h fee...

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Q: 1. (2x³y² + 4x?y + 2xy² + xy+ + 2y)dx + 2(y³ + x?y + x)dy = 0 %3D

A: note : as per our company guidelines we are supposed to answer only one question. Kindly post other ...

Q: 343 | lim x → 7 x – 7 - O - 28 O 147 O 98 O – 147

A: Topic:-  limits and continuity  

Q: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and lengt...

A: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and lengt...

Q: A microwave transmitter emits electromag- netic waves of a single wavelength. The maxi- mum electric...

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Q: Let us try to find where a function is increasing or decreasing given the following.  f(x) = x3−4x,...

A: Topic:- calculus

Q: Using the fomat of dy/dx below, find (A +B+C+ D). dy 40t? + At +B dx -Ct? + Dt + 3 ||

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Q: 5**+2x (2x3 +1)dx *(2x3+1)dx

A: I have stated the used formulas in the solution.

Q: 6. Given the space curve r(t) = (t, 2et, e2t), find the tangential and normal components of accelera...

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Q: Write an equation (any form) for the quadratic graphed below: 4- 2- -5 -4 3 -2 -1

A: Vertex =(h,k)=(2,1)From graph ,Parabola passes through points :(0,-1) &amp;(4,-1)std equation of par...

Q: Use sigma notation to write the Taylor series about I = 6 for the function. 1 Σ

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Q: Compute the first three non-zero terms of the Maclaurin Series for f(x) = ecos x

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Q: Determine the intervals on which the graph of y = f(x) is concave up or concave down, and find the x...

A: To determine the intervals on which the graph of y=fx is concave up or concave down, and to find the...

Q: The following bar graph shows U.S. math SAT scores as a function of household income.† A bar graph ...

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Q: 22. Find the required derivatives. a) y = (4x3 - 2x + 1)-2; find y b) x = Vy? + 1;find x"

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Q: Find the average value of f (x, y) = = 4x cos(xy) over the rectangle R = {(x, y) | 0 < æ < n, 0 < y ...

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Q: 2. Find the slope of the curve y? = 3x 1 at the point (-0). Draw the graph of !! the curve.

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Q: A hole of radius r is bored through the center of a sphere of radius R. Find the volume V of the rem...

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Q: 21. Find y' using implicit differentiation. a) In (xy + x + y) = 2 b) In (sin xy) = xy

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Q: A. (A +B+C+D+ E+ F) B. (P + Q +R+M + N) (x² + 1)(x + 1) (2x + 3)* dy or y': dx Ах' + Bx? + 2х + с Dx...

A: As per our guideline we are supposed to be answer only one question you can repost other questions i...

Q: x+1 dx 3. (25 – x²)3/2

A: Solve by separate integral

Q: Find the following limits i 1. 8x lim x>+* 5x – 7

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Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

Q: The function f is shown below. What is the value of | f(x) dx? Write your -4 answer in simplest form...

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Q: 2.2) Solve and explain the steps involved. (2+72)es*dr

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Q: Given: sing = - e is a third quadrant angle, and tand = - is a second-quadrant angle; find cos(e+ d ...

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Q: Evaluat..f.x.dA. wha.is.the..sgiem.in.the.fiigt. R quandrant..bounded..xy=16. X..8....y.z.. y.e.x...

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Q: Eliminate ARBITRATY CONSTANTS y = a²t² ; x =b + at

A: Given:To Eliminate ARBITRATY CONSTANTS y = a²t² ; x =b + atSince  we know that, number of independen...

Q: Find y' by implicit differentiation 1. x³+y³=6xy 2. x²+y²=4

A: Question 1,Given,           x3+y3=6xyTo find : Find y' by implicit differentiation.

Q: 3. x/1+x° 1 dx (use trigonometric substitution)

A: sec2θ -tan2θ =1 ∫cosec(θ) dθ = 12lncos θ-1cos θ+1+C