1 2 √x² x + 10x + 61 S -dx =

Q: Find the values of x, y and that correspond to the critical point of the function: z = f(x, y) = 4x²…

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Q: 4. Suppose a balloon in the shape of a sphere is being filled at a rate of 100 ft³/min. How fast is…

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Q: Electric charge is distributed over the rectangle 0 ≤ x ≤ 2, 1 ≤ y ≤ 4 so that the charge density at…

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Q: The Map As you walk through Gate 4, you realize that Gate 5 is nowhere to be found. In front of you…

A: Given f( x ) is continuous in the given domain If a function is continuois at x = a then limx→a-f( x…

Q: Q2 Find and simplify the derivative of f(x) = cosh ¹(sinh(x)).

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Q: Differentiate the function. h'(x) = h(x) = In(x + √x²-2)

A: Use the derivative of log function.

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: 4. Find the exact arc length of the curve over the stated interval: x=3t², y=t³,0 ≤t≤2

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Q: A lamina with constant density p(x, y) = p occupies the given region. Find the moments of inertia Ix…

A: Solution is given below:

Q: A movie theater has a seating capacity of 335. The theater charges $5.00 for children, $7.00 for…

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Q: Find an equation for the graph sketched below: -5-4-3-2 ME 6 S -2 -3 -4. 5 -6 -7 -8+ N a

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Q: Determine if the limit lim (1+5x) 1+0+ exists, and if it does, find its value.

A: Given: limx→0+1+5x12x

Q: The graph of y = f(x) has ƒ(5) = -2, f'(5) = 2, and f'(5): = -1. Which of the = −1 following might…

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Q: Suppose that f(x) = x³ - 6x² + 15. (A) List the values of all local maxima of f. If there are no…

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Q: Find the critical point of the function f(x, y) = −8+2x+4x² + 5y-y² This critical point is a:…

A: Given f( x, y ) = -8 + 2x + 4x2 + 5y - y2

Q: The Ninth Gate You arrive at the final gate, which leads into a building-like structure. You hope…

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Q: Complete the parametric equations of the line through the point (2,-6,-2) and perpendicular to the…

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Q: 43. y = (2+x)√2+(2-x)², [0,2]

A: Given function:- y=2+x2+2-x2

Q: = 1/₂ F² A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and…

A: We have to find the integral.

Q: do you know the formula for finding integrals

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Q: A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the…

A: Given: The angle of elevation of the plane is θ= pi/9 The distance (in meters) the ball bearing…

Q: 5. If 3x²z+y³-xyz³ = 0, find az / əx. 6. Show that if w=f(r-s,s-t,t-r), then dw dw dw dr + + = ds ôt…

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Q: 2. Determine whether the series is convergent or divergent. If it is convergent, find its sum. ܐ 5…

A: The Series ∑n=0∞arn is called geometric series and the geometric series a is the first term and r is…

Q: For what values of p does the following series n=2 (Inn)p-2 n converge or diverge?

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Q: Find √ √1 + x²dx

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Q: Find y if In X Jer X (2x + 7) dx +4% + +4x + 8 8 | + ² tan y + c

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Q: 3√t-1 S (³√t=¹) dt

A: The given integral is:  ∫3t-1t dt

Q: A ball is thrown into the air and its position is given by h(t) = −4.5t² + 87t + 19 where h is the…

A: Application of Derivative

Q: Find the derivate of the functions a) F(x) = (7x²-9) (2x + 7) f'(x) = b) f(x) = 8x² - 2 8x +3 f'(x)…

A: To find derivatives

Q: A company buys a machine for $275,000 that depreciates at a rate of 30% per year. Find a formula for…

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Q: п Convert the point (p, 0, 0)=(3, 377) 6 expressions, or decimals to at least one decimal place. (x,…

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Q: b) lim x² +8x+16 X-1 x²-16

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Q: The Sixth Gate After walking through the fifth gate, your computer informs you that more than half…

A: Given function f( t ) = 1a( 7t3 - 55t2 + 165 )40

Q: Evaluate the integral. cos y dy 2 sin y + 3 siny-4 S

A: To evaluate∫cosysin2y+3siny-28dy

Q: 4. Evaluate the limit, if it exists: lim x+1 a. 1 b. -1 x²-3x+2 x-1 c. d. 0 does not exist

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Q: a = (0, 1, 2), 128. c= (1, 0, 1) - b = (-1,

A: Given: a=0,1,2b=-1,0,1c=1,0,-1

Q: 2 √x (x + 1)² dx =

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Q: Using the ratio test to determine the convergence or divergence of the series series. O Convergent…

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Q: z is incorrect

A: We have to find the value of z (Round to 4 decimal)

Q: 4. a) Find the general solutions of the following differential equations. Express the general…

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Q: The Third Gate You arrive at the third gate and look for the inscription. Your computer translates…

A: For x approaching c from the left, x<c  ⇒  x-c5<0The denominator is a negative  approaching…

Q: Consider the function f(x) = 1−3x², -3 ≤ x ≤ 1. Use the derivatives to algebraically answer the…

A: Given, As per given question we need to find the extreme points of the function fx=1-3x2 on the…

Q: The number of cell structures in a Minbari stem cell (fictional) is modeled by f(t) = 1 + 30t - 10t³…

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Q: A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and write…

A: given shaded region is between concentric circles with radius r=8 and r=10. So, it is better to use…

Q: Question Graph the feasible region subject to the following constraints: 6x+8y > 208 x>8 y≥8

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Q: Find the exact absolute maximum and absolute minimum of h(t) = cos(2t) + √3 sin(2t) on [0,1]. Show…

A: h(t)=cos(2t)+3sin(2t)for critical points, put h'(t)=0d dt(sint)=costd dt(cost)=-sint

Q: let y = 3 x² + In x - ex find y' O 6x + (1/x) + ex O 6x - (1/x) - ex O 6x +1 + ex O none of the…

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Q: = 4y cos(2x - 5y) at the point (5,2,8) Find the tangent plane to the equation z =

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Q: determine if the mean value theorem can be applied to the function f (x)=x^2 on the closed interval…

A: we have given function f(x)=x2 which is continuous on the interval [3,9]. differentiation of this…

Q: Find the derivative

A: We are required to find the derivative of (a) y=cos2tan1+x3(b) f(t)=3csc5πt-71-cotπt5-7