Checkpoint 5.14 step by step

Q: solve the given initial value problem. 6x2y'' + 7xy' - 2y = 0, y(1) = 0, y'(1) = 1

A: The initial value problem is  6x2y''+7xy'-2y=0, y(1)=0,y'(1)=1 which is in the form of Cauchy Euler ...

Q: Use the vertical line test to identify graph (see attached) in which y is a function of x.

A: We need to use the Vertical Line Test to determine whether y is a function of x in the given graph o...

Q: find the solutions of the differential equations that satisfies the given initial conditions: (x^2+1...

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Q: 8.y″ + 6y′ + 13y = 0

A: Given differential equation: y''+6y'+13y=0

Q: Mixing problem Two tanks X and Y are interconnected (see figure). Tank X initially contains 100 lite...

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Q: Use equation to answer the following questions. y=(x-1)/(x^2) a. Find the domain b. Find the interce...

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Q: Find the derivative of the function f(x) = arcsin x + arccos x

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Q: Solve the equation: 3sin x - 2 = 5sin x - 1.

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Q: Consider the following limits of Riemann sums for a function ƒ on [a, b]. Identify ƒ and express the...

A: The limit of Riemann sum for a function on 1,2 is lim△→0∑k=1nxk*lnxk*△xk.  

Q: And the fellomng limit. find the fmleto C1-2ス) 12 276

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Q: Use the formula to convert the given Fahrenheit temperature to its equivalenttemperature on the Cels...

A: we have to use the formula to convert the Fahrenheit temperature to its equivalenttemperature on the...

Q: Evaluate the limit.

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Q: 3.

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts f...

Q: You need to rent a rug cleaner. Company A will rent the machine you need for $22 plus $6 per hour. C...

A: Given that: Company A will rent the machine you need for $22 plus $6 per hours. Company B will rent ...

Q: The velocity of a (fast) automobile on astraight highway is given by the function shownwhere t is me...

A: a. The graph of the equation v(t) is By looking at the graph, it is observed that velocity is zero ...

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

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Q: How do you solve linear first-order differential equations?

A: First order linear differential equations are in the form of dydx+Pxy=Qx. These equations can be sol...

Q: for B, why is n=4 incorrect?

A: Given: θ=sin-112n+1tanββ=15°n=4

Q: The figure shows the region of integration for the given integral. Rewrite the integral as an equiva...

A: The figure shows the region of integration for the given integral. Rewrite the integral as an equiva...

Q: Find the critical numbers of the function.                                                          ...

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Q: i need help please

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Q: This is a calculus 3 problem. Please explain clearly, no cursive writing.

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Q: The graph of my function is not a straight line, so I cannot use  slope to analyze its rates of chan...

A: given: the graph of my function is not a straight line , so i cannot use slope to analyze it's rate ...

Q: Please help and show all the steps. Consider the function f(x)=x^2−3x+2/ x+4 Find the first derivat...

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for ...

Q: sin? x 1+ cosx (b) Use part (a) to show that (a) Show that 1- cos x Cos x lim 1- Cos x [Hint: sin x ...

A: a. To Prove: 1-cos x=sin2x1+cosx Consider, sin2x1+cos x= 1-cos2x1+cos x      ... Using sin2x +cos2x=...

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C f...

A: f(x)=78+45x2-89x3

Q: How do I do this?

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Q: Qustions

A: 1. fx=1sinπx4 over the interval [0,1]and f'x=-π cotπx44sinπx4Now, f'x=0or, -π cotπx44sinπx4=0or,  co...

Q: Each limit represents the derivative of some function fat some number a. State such an f and a in ea...

A: Given: limh→01+h10-1h

Q: Find the indefinite integral in two different ways, (a) use a graphing utility to graph the antideri...

A: The indefinite integral, ∫sec2x tanx dx.

Q: Write the equation log5(x + 4) = 2 in its equivalent exponential form. Then solve for x.

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Q: 38. Calculate y = x, x = 0, and x = 1. || e* dA, where D is bounded by the lines y =x +1,

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

A: The function is y=x22-ln x4. Sketch the graph of the function as shown below.

Q: Use Table to evaluate the following definite integrals.

A: The given integral is: ∫0π16sec24x dx From the table given , ∫sec2ax dx =1atanax +C. ∫0π16sec24x dx=...

Q: I need help with b and c

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Q: graph f(x) = x2-3x-4/2x2+4x

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Q: x²+ kx - 24 Consider the function G(x) = to answer the following. x2-x- 12 A. Determine for which va...

A: The function G(x)=x2+kx-24x2-x-12. We have to find the value(s) of x for which the function is not c...

Q: use l’Hôpital’s Rule to evaluate the limit

A: we have to evaluate the given limit by using the L.hospital's rule: limx→∞5x2-3x7x2+1

Q: Find the horizontal asymptote, if there is one, of the graph of the rational function: f(x) = 12x/(3...

A: Consider the rule, for finding the horizontal asymptote of any given rational function. For any rati...

Q: can someone help please

A: We need to find out sine of 4 radian: In radians:sin4=−0.7568024953 correctIn angles:sin4°=0.0697564...

Q: Find the normal line to f(x) = ax 8ax at x= 9. Assume that a is a positive constant.

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Q: Find the critical numbers of the function  f(x) = x3 + 6x2  - 15x

A: Solution -  Given function is given as- f(x) = x3+6x2-15x                   ...........................

Q: Q

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st ques...

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.