Use the properties of logarithms to rewrite and simplify the logarithmic expression. In In 5 In 3 In 3 – 2

Q: Question 1 If z=lm/x*+ y² + un /x²+y²+-tan 12 then the numerical value of dy? dx2 is equal to...-

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Q: Fundamental Theorem: 2z Let f(x) = | Vcos t + t° dt . Find the value of f'(x). %3D 1

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Q: 8. Find the dimensions of the largest-volume cylinder that can be inscribed in a sphere of radius 10…

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Q: AB is the vector from the point (1, –2) to the point (5, 1). Find a unit vector in the opposite…

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Q: 2. Calculate the following limits. Justify your answer. L'Hopital's rule Rule ) (without using 2x +1…

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Q: onsider the functionfx) 5x" + 8x 1. f(x) has a critical point at x ind the value of A: A, does f(x)…

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Q: Find the value V of the Riemann sum V = f(ck)A¤k k=1 for the function f(æ) = x² + 3 using the…

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Q: Q.1/ Find the area of the region bounded by the line y = 1- x and the curve x = 3 - y2. Q.2/ Change…

A: Area bounded by the curves :  If f(y) and g(y) are two continuous function on a,b and f(y)≥g(y) on…

Q: Since u = x, then converting back to an expression in x we get

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Q: tan -x -dx is equal to ONE of the followir The integral (HINT: Use Maclaurin series) Σ n=0 2" +'(2n+…

A: Here is the solution

Q: cot(x) – cot(a) lim where a + na. е. x - a 10 f. lim +- n00

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Q: 4. ( Consider points P(1,0, 1), Q(-2,1,3), and R(4,2,5). (a) Find the parametric equations of the…

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Q: If f(x, y) = -x³ +y - 3xy + 9x2 +y, then in the of obtaining its critical points we obtain the…

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Q: 8. Given, h(x) = 2 – x and g(x) = -x²+ 4 a) Plot the two functions on the same graph for -2 < x <4…

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Q: 2 dx 6) dx sec x csc x 7) -4tan x dx 8) -cot x dx

A: 1. ∫2sec(x)dxWe know that 1sec(x)=cos(x)=2∫cos(x)We know that ∫cos(x)=sin(x)=2sin(x)+C 2. ∫5csc…

Q: Write down the solution of the differential equation: y +4y +3y x2 -5x +4 if y(0) = 0 and y (0) =1

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Q: The following data lists different investment amounts (X) and the amount of interest (Y): X5 Y 2.5…

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Q: A rectangular box with an open top is to be made from a 9-inch by 24-inch piece of cardboard by…

A: This question is based on application of derivative.

Q: Use series to estimate the lim m X-1

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Q: x* (x – 1)? (x + 2) (x² + 1)* Calculate the derivative by logarithmic differentiation: g(x)

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Q: QS: Find the first derivative at x = 2 for the function given by the data 1.0 1.5 2.0 3.0 0.4057…

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Q: dy 6. If y is a differentiable function of x and r + 2y3 x² = 8y?, then find dr

A: This question is based on diffrentiation chain rule.

Q: 3. Sketch the graphs of y = 4e -x, x = 4, x-axis and y-axis. Shade the region bounded by the curves.…

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Q: x2+3x-1 16. Use L'Hôpital's Rule to evaluate the limit lim Write o if the limit is infinite.

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Q: Compute the given integral. ICOS Idz +C

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Q: () 0.02x 26, ere a represents the level of production and C' (a) represents the margina items, the…

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Q: 33 3.

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Q: Differentiate 1)2xsin-13x x+1 2)y = In; Vx-2

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Q: 8) A rectangular storage container with a square base is to have a volume of 2250 inches cubed. The…

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Q: B2. dx Let g(?) = " 4t

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Q: 5. S sec(3x) tan(3x) dx

A: formula:∫ secx tanx dx =sec x +Cwe are given;I=∫ sec(3x) tan(3x) dx3x =t3 dx =dtdx =dt3

Q: For the following table, assume that y = a (x ^b). Then 2 7 9 11 11 17 13 25 y = 3.083 x^2.312 O…

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Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

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Q: Which of the following are equivalent to log, (4)? Choose all that apply. 1 log, (16) log, + log,…

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Q: Given the vector field F = (z,x, y), calculate the flux of the curl of F through the portion of the…

A: Given

Q: Question 3 > Use part I of the Fundamental Theorem of Calculus to find the derivative of 14 dt f'(x)…

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Q: Find the linear approximation of f(x) = Vx at xo = 27.

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Q: 6) Let sin 0 - for n <0 < Find the exact value of: %3D 2. a) cos 0 b) tan 0

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Q: Write the following sum as a single logarithm and fully simplify. Assume all variables are positive.…

A: Given :log4(35)+log4(y)-log4(7)

Q: where Sint yo teld y=ueat cast. U=-2 i t=0 and then dt.

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Q: 8. h(x) = (sin x )V tan²x + 1 %3D

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Q: The perimeter of an isosceles triangle is 38 m. Find the length of the sides of the triangle of…

A: Here we have the perimeter of the isosceles triangle = 38 m,  Let the equal sides of triangle = x…

Q: Find the slope of the tangent line to the curve - 32 + 2ry-y = 0 at the point ( 1, – 1).

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Q: 19. Find the equation for the line tangent to the given curve y f(x) at the point P. (a) f(x) =…

A: Given, f(x)= 2x²+5x-10 P=(x,y)=(1,-3)

Q: Let y tan(3x + 6). Find the differential dy vwhen a 2 and da 0.4 Find the differential dy when z 2…

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Q: 1 liter of paint that costs 200.00 pesos can cover 13.33 square meters, exactly how much will be…

A: This question can be solved using the concept of units and measurement.

Q: derivatives

A: We will solve the 2 problems.

Q: 3- -2 1- |-1 0 1 2 3 4 5 6 8 --1- t. --2- (a) Evaluate А (0), А(1), A(2), А(4), А(6), A(8). (b) On…

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Q: 4. 7 (t) = (4t, –2t, /5 t) = (4t, -21, v5 ') %3D

A: This is a problem related to vector differentiation. Based on the general formula we can calculate…

Q: (10) Which of the following is(are) true for the function f(x) = 2 - log3(x + 1) ? I. The x and y…

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