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Q: consider a ctosed Kectangutar box with a If base side ir measured with ekror at H.w.y squak bare and...

A: Write the formula for the surface area and volume and then apply total derivative. 

Q: Determine the surface area generated when a portion of the curve in the first quadrant of y? = 4 +x2...

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Q: Find the points on the graph of f(x) = where the tangent line is horizontal. x2+2

A: Given query is to find the points where tangent is horizontal.

Q: Write a rational function that has x=-2 as its only vertical asymptote, a hole on the line x=2 and a...

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Q: Determine the surface area generated when a portion of the curve in the first quadrant of y? = 1+ is...

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Q: Match the integral expression on the left to an equal expression on the right.

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Q: The derivative of the function y = log2(In(x)) is:

A: We can find the correct answer as below.

Q: If the vector field F = (sinx + (7 + c)xy, (c + 1)x² – e') is conservative, then c=

A: Given

Q: 1. What is the first thing to consider when finding the extrema of a function? A. Check the critical...

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Q: 4. Given the graph and function below, complete the table. Differentiable Continuous f(x) Derivative...

A: The given graph is f(x)=x2+1

Q: dy Find using implicit differentiation, for the equation a + y=8 is da O O

A: Differentiate both sides with respect to x.

Q: The coefficient of sin ( 2x) in the antiderivative of

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Q: Exercises: Find the general solution of the following differential equations 4) y"+2y'+y=3e*

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Q: In (1.06)

A: answer of given question is in step 2

Q: S cos?x-ex

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: Using an appropriate substitution, gtan-1 x the integral S dx equals: 1+x2 gtan-1x + C 4 tan-1x + C ...

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Q: Using an appropriate substitution, e*sec²(e*) the integral S dx equals: e-tan(eX) - In|e – tan(e*)|I...

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Q: If f(x) = 7 cot-l+ 5, then find the value of f'(-6) is -5 37 -6 37 O 00 O 7 37 O -7 37

A: Topic:- application of derivatives

Q: find eigen value of matrix A 3 -2 A %3D -니 2. 2.

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Q: Let a = ci + j and b = 2i + 10j. Find c so that a and b are orthogonal. c =

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Q: Determine the slope of the tangent line to the graph of ƒ (x) =- at the point(4, -4).

A: Use differentiation for finding the slope.

Q: 2. An open box will be made by cutting a square from each corner of a 6-ft by 6-ft piece of cardboar...

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Q: 1J"In xdx 1.5

A: Given query is to find the integral.

Q: Rewrite the following integral using substitution: " s in3xdx

A: We can rewrite the integral using substitution as below.

Q: BE F(x, y) = #ty? y I THE FIELD DEFINED IN %3D 1²+y² 1²+y? D = R? – {(0,0)}. CALCULATE $ F •d7, · d7...

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Q: An exponential function has a decay factor of 0.03. What is the percentage decay rate?

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Q: Eväluate the following. 1. ſ csc?dx 5

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Q: Write an equivalent double integral with the order of integration reversed. dy dx dx dy dx dy ©SS ax...

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Q: Using calculus, find three positive numbers whose sum is 12 and the sum of the squares is as small a...

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Q: For the demand function q= D(p)3D226-p, find the following. a) The elasticity b) The elasticity at p...

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Q: 8. arctan (-1)

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Q: az az Find and e = 5x 2² + sin(r + 2) – y?.

A: Find the partial derivative of z with respect to x and with respect to y respectively

Q: The solution of the non-exact differential equation (x*e +5dy + (1 +2x²e")dx = 0 is: O x^2 e*y+Inlyx...

A: To determine the solution of the following non‐exact differential equation.x3ey+xydy+1+2x2eydx=0

Q: At which point/s (value/s of x) is the function continuous but not differentiable? -4 2 4 6 8 10 12 ...

A: function is not differential at point where either its not differentiable or it has sharp point on c...

Q: Find the values of a and b if the tangent to y = ar² + bx at (1,5) has a slope of 8.

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Q: Florist Mehdi’s flower sales can be modelled by the function  f (t)  =  (7t + 8)e0.58t, where t is m...

A: We need to find average sales in % weeks.

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Th...

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Q: Calculus: In a certain city, the probability density function for x minutes to be the length of a te...

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Q: Compute the area of the surface formed when f(z) 2V1-z between -1 and 0 is rotated arou nd the -axis...

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Q: Provide an equation of one of the common functions with multiple transformations. For example, f(x) ...

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Q: logarithms to find an exact solution for   ln(5)+ln(5x2−3)=ln(154).   If there is no solution, e...

A: Given query is to find the value of x.

Q: Find the volume of the solid obtained by rotating the region bounded by y = x , y = 0, a about the y...

A: Given query is to find the volume finthe solid generated.

Q: a) dt 9 =dx xVln x b)

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Q: ng in such a way that its radius is decreasing at a rate of 0.3 cm/min. At wi wball decreasing when ...

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Q: 2. Complete the following tables of values to investigate lim f(x) f(x) -1 -0.8 0.75 -0.35 0.45 -0.1...

A: solution

Q: The solution of the exact differential equation (3x² + 4xy)dx + (2x² + 2y)dy = 0 is: None of the abo...

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Q: Evaluate the integral, if it exists: +z sinx dx z-

A: We will evaluate the integral if it exists in the following step.

Q: y = ecos²(x) is: eCos? %3D y' = - sin(2x)ecos²(x) y' = sin(2x)ecos²(x) the above the above y' = -2 s...

A: Here we will find the derivative of the given function,

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. Š(- 1)*+'6 k! ...

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