Find using substitution: y = cos"(x* + 1)

Q: Find f[g(x)] and g[f(x)] for the given functions. f(x) = - x° +5, g(x) = 4x + 6 %3D

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Q: Evaluate using Partial fraction method 5x² +27x + 12 dx -dp- x² – 5x +6

A: Here, the integrand is not proper rational function, so, we divide 5x2 + 27x +12 by x2-5x +6.  

Q: Second derivatives For the following sets of variables, find all the relevant second derivatives. In...

A: It is given that fx,y=ex-y where x=s2 and y=3t2   Second derivatives ∂2f∂s2=fss=fxxxs2+2fxyxsys+fyyy...

Q: Find the intervals of concavity and the inflection points.  f (x ) =  x/ x 2 +1

A: Given: fx=xx2+1 for finding intervals of concavity and inflection points, we draw graph of given fun...

Q: graph the function and find its average value overthe given interval. ƒ(t) = t2 - t on [-2, 1]

A: Graph of the function: f(t)=t2-t  ; [-2,1]

Q: What equations relate polar coordinates to Cartesian coordinates? Why might you want to change from ...

A: Equations relate polar coordinates to Cartesian coordinates are, x=rcosθ & y=rsinθ

Q: What does net area measure?

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Q: Let f(y) -8+ In Determine the derivative f'(y) : ||

A: The function is given as, fy=-1-8+lny. The derivative of the function , f'y=-0-0-8+lny2=0. The funct...

Q: Implicit differentiation Use Theorem 15.9 to evaluate dy/dx. Assume each equation implicitly defines...

A: The given equation is x2+2xy+y4=3. Consider Fx, y=x2+2xy+y4-3. This implies that, Fx=12x2+2xy+y4 2x+...

Q: Evaluate the limit using l'Hôpital's rule: - co X) lim 3x2

A: Differentiate two times with respect to x

Q: The slope of the normal line to the tangent line of 1 is f(x) = (sin x)² at a = V2 :Select one V2 .a...

A: We have to find slope of normal to the tangent line of fx=sin-1 x2 at x=12. We know the slope of nor...

Q: If a function ƒ(x, y) has continuous second partial derivatives throughout an open region R, must th...

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Q: Tangent planes Find an equation of the plane tangent to the following surfaces at the given point.

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Q: Find the lengths of the curves. If you have graphingsoftware, you may want to graph these curves to ...

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Q: Find the work done by the force field F(x, y) = xyi+ x²j on a ,2 particle that moves along the curve...

A: Consider the given force field Fx,y=xyi+x2j Then, F⇀x,y=xy,y Write in parametric form y=t  then  x=t...

Q: The estimate √(1 + x) = 1 + (x/2) is used when x is small. Estimatethe error when | x | < 0.01.

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Q: x +6 x2 – 6x +9 The given proper fraction can be resolved int partial fraction of the form O a. Ax +...

A: Explanation of the solution is given below....

Q: What will be the sequence generated by the generating function 3x/(1-x)2?     a) 9, 12, 15, 18...

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Q: Use a calculator’s factorial key to evaluate the expression: 54!/(54 - 3)!3!

A: To evaluate54!54 − 3!3!

Q: Solve the problem in a paper and upload as a pdf document. .3 Evaluate the integral SIT w?yz+v² xz +...

A: Solution: The objective is to evaluate the given integral

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: the given integral is: ∫065dx25x2+36 we have to evaluate the given integral.   let the given integra...

Q: Prove that ∣cos a − cos b∣ ≤ ∣a − b∣ for all a and b.

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Q: Use an identity to find the value of the expression sin 1.7 csc 1.7. Do not use a calculator.

A: To find The value of the expression sin 1.7 csc 1.7

Q: Q3 Integrate using trigonometric substitution: dx I To +x² /9 +

A: Let (x/3) = tant Differentiate on both side  dx/3 = sec2t.dt dx = 3.sec2t.dt

Q: (a) Prove that the equation has at least one real root.(b) Use your calculator to find an interval o...

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Q: Find parametrizations for the line segments joining the points. Draw coordinate axes and sketch each...

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Q: Find the domain of the function : f(x) = (7x + 2) / (x3 - 2x2 - 9x + 18)

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Q: Insert either <, >, or = to make a true statement 8/13÷8/13    | -1|

A: We have to insert <, > or = for  813÷813 and -1 We know that ab÷ab=ab×ba=1 or a÷a=1 If we divi...

Q: Trigonometric substitution x = tan 0, dx = sec20 d0

A: We have  x=tan θ Differentiating both sides with respect to θ, dxdθ=d tan θdθ=sec2θ Since, derivativ...

Q: I used the graph of y = 3 cos 2x to obtain the graph of y = 3 csc 2x.Determine whether the statement...

A: I used the graph of y=3cos2x to obtain the graph of y=3csc2x. Determine whether the statement makes ...

Q: A hot air balloon rising straight up from a level field is tracked by a range finder 150 m from the ...

A: A hot air balloon rising straight up from a level field is tracked by a range finder 150 m from the ...

Q: If rAB = -7i + 3j + 8k and A is the point (-2, -3, 6), find B.

A: Given that AB=-7i+3j+8k   and  A=-2, -3, 6. Consider them as AB=-7i+3j+8k   and  A=-2i-3j+6k. Comput...

Q: Find the volume of solid generated by revolving y = between x=1 and x=2 about x-axis O a. square uni...

A: The solid is obtained by revolving the region enclosed by the curve y=3x2 between x=1 and x=2 about ...

Q: Factor the perfect square trinomial: 25x2 + 10x + 1

A: Given: 25x2+10x+1 we know that a2+2ab+b2=a+b2                                                  ..1

Q: Solve the system xy = 4, x2 + y2 = 8 by the substitution method.

A: Given equations are: xy=4                              ⋯1 x2+y2=8                           ⋯2 From ...

Q: I More on Solving Equations Solve the equation for the variable x. The constants a and b represent p...

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: Illustrate what are the intersections of polar curves?

A: Question- Illustrate what are the intersections of polar curves? Answer- If the equations are rectan...