Q4: Answer two only: 2 1 -1 (A): I A=2 -2 Find AB and AC : - 1²/2 3 11 -2 -2 and 2 -- }

Q: Use the substitution u= x² + 6 to find the following indefinite integral. Check your answer by…

A: To evaluate the integral.

Q: Find a differential equation of the following family of curves whose solution is: 1. A family of…

A:

Q: Rewrite the expression In 3 + 5 ln x + 6 ln(x² + 4) as a single logarithm In A. Then the function A…

A: We know the property of logarithm that  ln(a)+ln(b)= ln(ab)  ...(1)  And,  pln(x)= lnxp .....(2)…

Q: For the given function, find all values of cover the interval (1.15) stipulated by Rolle's Theorem…

A:

Q: (B): Find the tangent equation to the curve y = sin² x at point x =

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

Q: cos¹3 xdx 2. Dễ sin12xcos®xdx 1.

A:

Q: Find all critical points of the following function. f(x,y) = 10x²-5y²

A: Please see the below picture for detailed solution.

Q: Write a polynomial f(x) that meets the given conditions. Answers may vary. Degree 3 polynomial with…

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Q: (B): Find the unit vector 3i - 4j + 5k perpendicular to the vectors: 4i + 5j-6k

A:

Q: 2 The function f(x) ==, x0, is one-to-one. X Find an equation for f(x), the inverse function. ...…

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Q: y"+y=t y'(0) = -2 y(0) = 1

A: The differential equation is given by      y'' + y = tThe auxiliary equation of the corresponding…

Q: Σ(1-1) η n +1

A:

Q: Calculate the distance between the point Q(3, 1, 7) and the plane 2x - 6y – z = 3. Don't use a…

A: We need to calculate the distance between the point Q3,1,7 and the plane 2x-6y-z=3 without using the…

Q: The equation u, 2uxx is a partial differential equation in one variable an ordinary differential…

A: Here we will find the correct option,

Q: Find the minimum and maximum values of the function on the given interval by comparing values at the…

A: Find critical points by putting derivative of given function equal to zero

Q: 4. What is the length of the latus rectum of the ellipse whose equation is (x-3)² + 2 = 1. 25 16

A:

Q: Find the limit, if it exists. If the limit does not exist, explain why. limx→∞((√x^2+2x) −x) You…

A: Given :limx→∞x2+2x-x

Q: Consider the points A=(1,2,3), B=(-2,1,0), and C=(0,3,1). Adding the vectors, find 2AB+3AC.

A: To find 2AB +3 AC

Q: Which of the following statements is/are true based on the graph of the function f(x) = -2(-x-²) +…

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Q: 5: Find the volume of the solid which is generated by rotating the region bounded by y=√x, y=x-2 and…

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Q: The region is bounded by the graphs of the equations y = sin x, y = 0, x = 0, and x = π. dA = ( A =…

A: Here is your solution

Q: If R is the region bounded by the graphs of the functions f(x) = 2 + 5 and g(x) = x + ½ interval [1,…

A:

Q: (B): If A = 2i + 3j - 4k; B = 3i-4j+ 5k and C = i + j - k, find: (iv) (3A + 4B). C (1) A.B (ii) B.C…

A: The objective of the question is determine the addition and dot product of given vectors.

Q: Find the derivative. G(t) = sinh(ln(t))

A: Topic = Derivative

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x sin²x (2) lim, o…

A:

Q: Compute u v if u and v are unit vectors and the angle between them is

A: topic- dot product of vectors

Q: compound proposition (PnQ)-(PUQ) is a

A:

Q: The direction field of the DE y' + ye³x+7 = −2y² will have a line segment with positive slope at the…

A: Given: y'+ye3x+7=-2y2

Q: 2. What is the radius of the circle defined by x + y² - 6x + 4y - 1 = 0

A: x2 +y2 -6x +4y -1 = 0 here we have to find radius standrad form of circle is (x-a)2 + (y-b)2 = r2…

Q: 9. (x²-x+y) dx - x dy = 0 10. (2y² + 2y + 4x²) dx + (2xy + x) dy = 0

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Q: The masses m, are located at the points P₁. Find the moments Mx and My and the center of mass of the…

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Q: Evaluate the following integral. 45 S SS²² dz dx dy -411

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) xy - 25 lim (x, y) → (5, 5)…

A:

Q: Find f if f"(x) = 2 + cos(x), f(0) = -1, f(π/2) = 2. f(x) =

A: Find f if f"(x)= 2+cos(x), f(0)= -1 , f(π/2)= 2

Q: Find the first partial derivatives of the following function. f(x,y)=x²-3xy-6y²

A:

Q: Q2: Solve the following integrals: (1) 7x²+14x+15 (x²+3)(x+7) dx ; (2) sinx+cos x sin³ x cos³ x

A: Since multiple questions are asked, I am answering first question

Q: 2π π +][im [[(sinx + cosy)dxdy πο 5.

A:

Q: Let g=yf(xy). Show that: - მყ У ӘУ дд - X- = g дх

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Q: Compute the partial sums S2, S4, and S6 of 1 1 + 5.6 6.7 (Use symbolic notation and fractions where…

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Q: Discuss the continuity of the function. 41 √x² + y² + z² f(x, y, z) == continuous except where x² +…

A: The given function,   fx,y,z=41x2+y2+z2

Q: e (5-x) dx = xydy

A:

Q: Find the limit, if it exists. If the limit does not exist, explain why. limx→∞ x / √x^2+x+1

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Q: 13. 2ny(8- y³/2) dy A) 4² (14 — y³/²) + C 7 2my 7 (14-y3/2) + C C) B) T² (14+y³/2) + C 7 D) 4²…

A: 13. The given integration is: ∫2πy8-y32dy To evaluate the given integral.

Q: 3. Find the Laplace transformation of the function: f(t) = cos (2wt) cos (3wt). Hint: write cos(20t)…

A:

Q: The pH can be calculated using the equation pH = -log(H"), where H" is the hydronium ion…

A: We can find the hydronium ion concentration as below.

Q: y = sin(x), y = 0, x = 0, x = Exercise (a) the volume of the solid formed by revolving the region…

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Q: The answer above is NOT correct. Find the area of the region enclosed between y = 4 sin(x) and y = 3…

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Q: Find the general isolation of the following: 1. (x³y³+1)dx +x4y²dy=0

A: Please see the below picture for detailed solution.

Q: 8 If f(x) = 3 + = + x 6 x2 find f'(x). Find f'(4). Round to 3 decimal places if necessary.

A: Given that f(x)=3+8x+6x2-(i)Our Aim is to find f'(x) and f'(4).

Q: the displacement is correct, but the distance is wrong

A: The velocity function is v(t)=-t2+6t-8 on the interval -3,5