Use chain rule to find the derivative of the following functions: a. y = sin(5x) b. y = cos(x²) c. y = (2x + 5)¹⁰

Q: Find the general solution of the homogenous differential equation 9y" - 30y' + 25y = 0.

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Q: Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

A: Since you have asked multiple sub parts in a single request so we will be answering only first three…

Q: a) Prove the following: If f(x) is an integrable function with antiderivative F(x), and a, b are…

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Q: For what value of a is the following function continuous at every x? f(x) = x²-30, x<10 x≥ 10 ax,…

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Q: a) x2+5x-14 x²+8x+7 + x²-4x+4 3x²-6x

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Q: Evaluate the following limits algebraically. 1. lim x---> 2      {5x - 7; x = 2

A: Note:-Since you asked multiple questions according to our polcy we can answer only first question…

Q: 1) Analyze the function f(x)=x² In(x). Report extrema, inflection points, intervals of monotonicity…

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Q: Using rectangles whose height is given by the value of the function at the midpoint of the…

A: The given function in the interval .The aim is to find the area under the curve using the midpoint…

Q: Use implicit differentiation to find the equation of the tangent line to the function defined…

A: The given equation is; 6x2+2x4y5=8Point (-1,1)

Q: Evaluate the integral: 0 x = (A) Which trig substitution is correct for this integral? Ox= 16 sin(0)…

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Q: Find the volume of the region under the surface z=xy^2 and above the area bounded by x=y^2 and x+y=2

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Q: In the following exercises, use a change of variables to evaluate the definite integral. 2 294. ² t…

A: By changing the variables, to evaluate the following definite integral.

Q: 4. n=1 ne-n

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Solve the initial value problem If the solution is y = co + C₁x + ₂x² + C3x³ + C4x² + C5x5 +C6x6 +…

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Q: A projectile is launched straight into the air with initial velocity vo = 92 ft/sec. This tells us…

A: Given a velocity function v(t) The total distance travelled in the interval [a,b] is given by.

Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= 8 cos 0+6…

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Q: By recognizing each series below as a Taylor series evaluated at a particular value of x, find the…

A: A.1+6+622!+633!+644!+⋯+6nn!+⋯

Q: 20. What value of x will give the maximum efficiency of a screw with a coefficient of x-μx² friction…

A: Given that, a friction coefficient  .We need to obtain the value of x for which we get the maximum…

Q: Determine the amplitude, period, and phase shift for the given function. - cos(2x - 5) y=1- 1…

A: To determine the amplitude, period, and phase shift for the given function.

Q: Evaluate the integral: O x ○ x = 3 sec (0) 0x = 8 sin(0) (A) Which trig substitution is correct for…

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Q: The Taylor series for f(x)=x³ at 3 is Σen(x-3)". Find the first few coefficients. Co C1 C2 C3 C4 =…

A: The given function is The Taylor series

Q: Assume that y is the solution of the initial-value problem 5 sin x If y is written as a power series…

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Q: 14. A rectangle has its base on the x-axis and its upper two vertices on the parabola y =12-x². What…

A: The second derivative test states thatWe use this to solve the given problem.

Q: find the limit if it exists, or show that it does not exist.  lim (x,y)→(0,0) (x^4 −y^4)/x^2+y^2

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Q: derivative In 2 x-1 2 x+1

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Q: 2 0 0 1 -2 1 0 4 -3

A: given matrix is ,

Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis. x = a cos³…

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Q: Find the indicated term of the binomial expansion. (√2₁² +1³); second term 3 u

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Q: Find the slope of the tangent line to the graph of the polar equation at the point specified by the…

A: Given that the polar curve

Q: Determine the radius of convergence, R. R = 1

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Q: Monte Germany: Attempt 1 Which equation is correct? 4x^(3)(6x^(2))=10x^(6)

A: 4x^(3)(6x^(2))=10x^(6)is correct?

Q: 18. Find the volume of the largest right cylinder that can be inscribed in a cone of height 20.00…

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Q: The system of differential equations : has the solution Y C₁ et V₁+ C₂ e¹₂ V₂ + C3 e¹³ V3 where (in…

A: Given that

Q: 16. Split the number 15 into two parts so that the product of one part and the other is maximized.

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Q: at the point (0, 1/2). and b = The equation of this tangent line can be written in the form y = mx +…

A: y=1/[3sinx+2cosx]Point (0,1/2)

Q: Set up and evaluate the triple integral in spherical coordinates needed to compute the volume of the…

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Q: Convert the point with cylindrical coordinates 11π 13, 5 to Cartesian coordinates. Enter your answer…

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Q: Estimate the average value of f(x) from x = a to x = b. 28 21 f(x)

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Q: dr Evaluate the integral: 2² (A) Which trig substitution is correct for this integral? Or=2 sin(0)…

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Q: f(x) = ln(x)

A: A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x−a)k

Q: f(x) = (5z – 3)(4: 6(2-0³) 3-20 f(9) = 3 ၁၂ နှ

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Q: Find the indefinite integral of the function g(x)=e^(2x) sin(3x)dx

A: The objective of this question is to find the indefinite integral of the function g(x) = e^(2x)…

Q: 12x 8 °-x X ³/₂ dx 3

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Q: per 59. Mixing Nuts A store sells cashews for peanuts for $1.50 per pound. The manager decides to…

A: Cashews cost =$5 per pondpeanut cost=$ 1.50 per poundmixture cost=$ 3 per pound

Q: √ 5x(x² +4)√√x² + 4 dx. 2

A: To evaluate the following integral.

Q: Compute the matrix exponential eAt for the system x' = Ax given below. x₁ = 16x₁ - 16x2, x 2 =12x₁ -…

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Q: 5. Use Part one of the fundamental theorem of calculus to find the derivative of the following…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: List the first five terms of the sequence. a1 = 5, 2n + 1 2an +4 а1 а2 аз ад a5

A: To list the first five terms of the following sequence.

Q: Derive the formula of a circle using horizontal strip

A: We need to derive the formula of the area of a circle by using horizontal strip

Q: f(x) = 3x² (x - 2)²

A: f(x)=3x2(x−2)2We know that the Mclaurin series of 11−x11−x=∑n=0∞xn