(B): Find the tangent equation to the curve y = sin² x at point x = T-3 π .

Q: Question 20 Given the equation −4x² + 8x − 4y² − 56y − 4z² + 32z = −312 - a) Show that the given…

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Q: 3. 2 洲 dx

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Q: P 3. Evaluate the integral fx cos(3x²) dx as an infinite series. (You do not need to find the radius…

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Q: QUESTION 2 The equation ut = 2uxx is O a partial differential equation in one variable O an ordinary…

A: Given: ut=2uxx

Q: Q5: Find for the following functions: dx (1) In (x - y) = xy + y³ ; (2) y = tan³√/cot(7x);

A: Given :lnx-y=xy+y3y=tan3cot7x

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

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Q: The line graph shows the average number of awakenings during the night for men and women of…

A: To find the difference between the average of awakening during the night.

Q: cos θ = 5/13 , θ lies in quadrant IV Find sin 2θ.

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

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Q: A cylindrical tube expands as its radius r and height h increase at the rate of 2 in/min and 4…

A: Basic product rule of differentiation is used.

Q: Question [ a) [ b) s]: Show all your work. : Evaluate then find f(x). c) ¹ [(x+3) √/x-3dx J: If 1 […

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Q: Given f(x) = - 12√x + fractions. f'(x) = The domain of f'(x) is 20 X 18, find f'(x) and its domain…

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Q: 3 여 x 3

A: Given: 121-111231X=0-21

Q: Discuss the continuity of the function. f(x, y, z)= sin(z) ex + ex continuous except at (0, 0, 0)…

A: Our Aim is to discuss the continuity of the function given below:-f(x,y,z)=sin (z)ex+ey -(i)

Q: 2. Find the volume of the solid generated when the region between y = sin x and y = 0 for 0 ≤ x ≤ π…

A: The region between y=sin x and y=0 for 0≤x≤π is revolved about the y-axis.

Q: Evaluate the function at the given values of the independent variables. Simplify the results. g(x,…

A: We can solve this as follows:

Q: dw (C): If w = tan x and x = 4t³ + t ; Find ? dt dy

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Q: The volume of the solid obtained by rotating the region enclosed by y = 1/x³, y = 0, x = 3, x = 4…

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Q: Apply Descartes' Rule of Signs. Determine the number of possible positive and negative real zeros…

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Q: Evaluate xdx A√²+x+1-³x+2+ √(x + 2)² +²1+C B. √² + x + 1 - ² 1 x + ³ + √(x + 2)² + ² 1 + C…

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Q: In Exercises 37-42, use the Shell Method to find the volume obtained by rotating region A in Figure…

A: See this solution in below

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 3 cos(t)i…

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Q: Find d7 dx> d7 dx7 -(46 In(x)). -(x6 In(x)) =

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Q: the maximum and minimum values of the function f(x) = 6 sin(x) cos(x) + 10 on the interval [0, by…

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Q: Q4: Answer two only: 4 2 2 1 -1 1 (A): If A = -2 Find AB and AC. 01 0; 2 B = 2 -1 3 -2 -2 and 2 1 3…

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Q: Use logarithmic differentiation to find the derivative of the function f(x) = (sin 7x)/x c) Coal is…

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Q: | dx X æ /æ2+100

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: Find the indicated limit by using the limits 6f(x, y) lim (x,y) → (a, b) g(x, y) lim (x,y) → (a, b)…

A: Given: lim(x,y)→(a,b)f(x,y)=3lim(x,y)→(a,b)g(x,y)=-5To find:lim(x,y)→(a,b)6f(x,y)g(x,y)

Q: 4. A one-way road has an overpass in the form of a semi-ellipse, 15 feet high at the center, 40 feet…

A:

Q: A box with a square lid uses a material for the lid and bottom that costs $ 4.00 per square meter,…

A: We can solve the given problem by using the second derivative test.

Q: A rectangular box with an open top has a length of x feet, a width of y feet, and a height of z…

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Q: Which radical function has a domain of (xe Rx≤3) and range of (y e RIy2-4)? Oy--√x+3-4 Oy--√x+3+4…

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Q: What is f'(x) given the integral function •5x+1 f(x) = 5x+¹ cos(e") du? ○ f'(x) = 5 cos (es) o f'(x)…

A: We have to find out derivative

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

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Q: If the L[ eatsin3t ] = a/( s² + bs + 42), determine the value of b.

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Q: Given that 2 ≤ f(x) ≤ 4 for 4 ≤ x ≤ 5, estimate the value of 5 0³/ [ f(x)dx 5 [²₁ <5 f(x)dx

A: Given 2≤f(x)≤44≤x≤5To find range of∫45f(x)dx

Q: 3. 31 √ √(²x- (2x - 4y)dydx 1 -1

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Q: 2) Consider the DE: y" + 25y = 0 A) Verify that y = C₁ cos 5x + c₂ sin 5x is a solution of the given…

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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

Q: J 4 sin xecos* d.c

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Q: A particle moves along a straight line from the origin (O) with an initial velocity Va=6ft/sec and…

A:

Q: Q5: Find dx for the following functions: (3) y = ex.sin² x In√x

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Q: Consider lim (x,y) → (0, 0) xy 20 X (see figure). 20 20 (a) Determine (if possible) the limit along…

A: Here to determine, lim(x,y)→(0,0)x2+y2xy

Q: Question Find the angle, in degrees between 0 and 360°, which intersects the unit circle at the…

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

A:

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: 3. (x³+xy²-y)dx + (y³+x²y+x)dy =0

A: We need to find the solution for (x3+xy2-y)dx+(y3+x2y+x)dy=0

Q: H.W: Evaluate the integral 1. 30 [ (x²y - 2xy)dydx 0-2

A: Given: ∫03∫-20x2y-2xydydx