Evaluate: sin ycos ydy. sinºy A siny +C 8. 6. sin y sinsy + C 8. sin°y sin'y + C 8. - 6. sin'y + C 8. sin6y D 6. none of the given choices

Q: Evaluate the definite integral 7 (18x? – 2x + 9) dæ 3

A: Given,            ∫3718x2-2x+9dx

Q: Find the values of a and b if the tangent to y = ax² + bx at (1,5) has a slope of 8.

A: We can find the value of a and b as below

Q: dy Find using implicit differentiation, for the equation x° + y° = 10 is da %3D y7 y5 y5 o O O O

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

A:

Q: Check if the field is conservative, if so, calculate by the Fundamental Theorem of Calculus for Line...

A:   F =2xy i +(x2+2yz) j + y2 kcurl F=ijkddxddyddz2xy(x2+2yz)y2      =(2y-2y)i-(0-0)j+(2x-2x)kcurl F =...

Q: Using an appropriate substitution, 3 the integral S dx equals: V1-4(x-1)2 3 sin-1(2x – 2) + C sin-1(...

A: We can find the integration as below using proper substitution.

Q: Which of the following best describes the function below? S (x) ={** if.rso |-r² if 0 <.x A. Continu...

A: To find out the correct statement. 

Q: Find  dy du,  du dx, and  dy dx. y = 2   u,     u = 5x + 3

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Q: State the domain, vertical asymptote, and end behavior of the function.   g(x)=ln(4x+24)+1.1   E...

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Q: The derivative of the function y = sin-1(ex – In x), where Je* – In x| < 1, is:

A:

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: Using integration by parts, the integral Vx In x dx equals:

A: Given ∫1ex lnx dx To evaluate integral using by parts rule

Q: The population of a certain species is given by N = 127 × 1.06t, where t is measured in years. What ...

A:

Q: 4 Find the value of f'(-1) if ƒ (x) =. (3xr² – 2x +1)

A: we have : f(x) = 4(3x2-2x+1)3 To find :f'(-1)

Q: 1. Find the derivative for each of the following functions Simplify and factor when possible! a) g(x...

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Q: Find the arclength of y 2x3/2 on 1 < x < 3

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Q: Determine if the integral is convergent or divergent. Evaluate the integral if it is convergent. Sup...

A: To solve the following integral

Q: Find the volume of the solid obtained by rotating the region bounded by y = x, y = 0, and x = 4, abo...

A: The given problem is solved below in detail.

Q: The derivative of the function y = log2(In(x)) is: 1 1 y': x In 2 In x y' = x In 3 ln x the above th...

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Q: By completing the square, dx the integral S equals: 2x2+8x+10 tan-1(x + 2) + C : tan-1(x – 2) + C th...

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Q: If f(x) = 6 cotlx + 8, then find the value of f'(-2) is %3D -2 -8 V5 8. OO O

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Q: The solution of the given equation (1+x²) y' + 2xy = 4x² is: O y=[(4x^3)/(3(1+x^2))]+C(1+x^2) O y=[(...

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Q: Calculate the curvature of the vector function when t= -7: 7(t) = (1+ 2t, 7 – 3t, -8 + 5t)

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Q: 1. Use the 8 step algorithm for curve sketching to analyze the key features of the following functio...

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Q: A bakery works out a demand function for its chocolate chip cookies and finds it to be q = D(x) = 95...

A: Given that, The demand function is following, q = 950 - 14x Where x is the price and q is the demand...

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

A:

Q: The derivative of the function y = e* In(cos x) is: y' = e*(In(cos x) – tan x) y' = e* (In(sec x) + ...

A: Use the derivative of the form y = u.v

Q: e ( + 4)2 dx = Evaluate the integral if it converges. Enter the exact answer, or enter na if it dive...

A:

Q: Find the relative extreme of the function f (x) 12+2x+2 and where they occur.

A: Given: - The function is, f(x)=x+1x2+2x+2 To find: - The relative extreme of the given function.

Q: why should y>0 ?

A:

Q: e2 6. - dx -Find 1

A:

Q: What is the formula that would be used to calculate the trapezoid approximation of s82x dx using fiv...

A: we have to approximate the value of integral by using trapizoid rule

Q: company makes computer chips from square wafers of silicon. It wants to keep the side length of a wa...

A: Find your answer below 

Q: If g is continuous at a and f (x)=(x² -a' )8(x). fir find f'(a). Hint: Use f'(x1) = lim S(x)-f(x,) %...

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Q: 34x + 16 f(z) g(z) The partial fraction decomposition of 8x2 can be written in the form of - 14x + 3...

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A: To find out the distance from point P to line AB. 

Q: er the following function and express the relationship between a small change in x and the correspon...

A: Topic:- application of derivatives

Q: DO NOT include spaces in between characters. * d (y -8 de (y° +8 Compute at x =2.

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Q: Suppose that the functions h and f are defined as follows. h (x) = x? -9 f(4) = 2 Find the compositi...

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Q: If f(x) = 7 cot ' + 5, then find the value of f'(-6) is -5 V37 V37 37 -7 37

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Q: 700 find the following. For the demand function q = D(x) = - a) The elasticity b) The elasticity at ...

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Q: Using integration by parts, the integral 2 f cot-1 x dx equals: 2 x cot-1x+ In|x² + 1| + C - x cot-1...

A: Given problem:- Using integration by parts solve 2∫ cot-1(x) dx 

Q: Calculate thex and y components of the vector given below. Do not round any intermediate computation...

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Q: tan x+ cot x csc(2x) = %3D

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Q: Scse (2x + 1)dx CSC

A:

Q: Using an appropriate substitution, eXsec²(e*) the integral S dx equals: e-tan(e*) - Inle – tan(e*)I+...

A: This question is based on indefinite integral.

Q: 5. Determine the slope of the tangent at point (1,5) on the graph of f(x) = (9 – x²)} + 1.

A:

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

A: Given

Q: Determine the Riemann sum that represents the illustration below. The function is lx) = 2x. Y 6. 4- ...

A: Explanation of the answer is as follows

Q: spac characters. * d Compute de y -8 at r =2. y +8

A: Topic:-  derivatives