dy + p(x)y = q(x), p(x) • q(x) # 0 dx

Q: Verify the identity: (sec t + 1)/tan t = tan t/(sec t - 1)

A: Multiply the left side of the equality by (sect-1) in the numerator and the denominator. 

Q: Find an equation of the tangent line to the curve at each given point. x = t2 − 4,    y = t2 − 2t ...

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Q: Explain why

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Q: Evaluate x2 - 2x + 5 for x = 1 - 2i.

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Q: Find dydx.   y=−30x5 dydx=

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Q: Evaluate

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Q: (B) At point (1,5), Find the Vector that is tangent and Normal to the curve: X' = 2y + 10

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Q: Solve 3x - 2y = -5, 4x + y = 8 by the method of your choice. Identify systems with no solution and s...

A: From 4x+y=8 we get y=-4x+8  Then we plug it in 3x - 2y = -5  

Q: Most scientific calculators have keys for log10 x and ln x. Tofind logarithms to other bases, we use...

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Q: Use the given graph to estimate the value of each derivative. y= f(x) 1 (a) f'(0) (b) f'(1) (c) f'(2...

A: Given, The graph of function y = f(x).

Q: Find the limit

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Q: How can an elementary function be represented as a power series?

A: An elementary function can be represented by using Taylor series expansions. We use successive deriv...

Q: What does it mean if a function f is increasing on an interval?

A: Let the given function be y = f(x) And the interval be I.   

Q: Determine if the given relation y=3x3+x is symmetrical to the x-axis, y-axis, the origin, or none.

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Q: In the equation 6x2 -7x-3/2x2-7x+6 Determine the point at which the graph of R intersects the horizo...

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Q: find the volumes of the solids generated byrevolving the regions about the given axes. If you think ...

A: Given that: The curve   x = y - y 3 To find the volume of the solids. To sketch the region in the fi...

Q: Fill in the blank/s : If f is a polynomial function of degree n, then the graph of f has at most____...

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Q: A function is given by a table of values, a graph, aformula, or a verbal description. Determine whet...

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Q: Find the derivative of the following function.   y=9x−52+10x−12+x3−7 y′=

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Q: Important limits Complete the following table and give approximations

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Q: Using logarithmitic differentiation, find the derivative of y=x^2(x+1)^4/e^x^2

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Q: Graph equation in a rectangular coordinate system. 3x - 18 = 0

A: We first solve the equation for x. 3x - 18 = 0 3x=18 x=6   Then we make a table for the equation. ...

Q: Use a graphing device to approximate to two decimal places, the value of x where the graphs of the e...

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Q: ) lim (Vx+3 +Vx) 14

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Q: What is the natural exponential function?

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Q: Let v = i - 5j and w = -2i + 7j. Find the specified vector or scalar v + w.

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Q: The temperature T of a person during an illness is given by T(t)=3tt2+2+98.6​, where T is the​ tempe...

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Q: Hw 3.1 Q 26

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Q: Two runners, starting at the same location, run along a straight road for one hour. The velocity of ...

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Q: Determine whether each integral is convergent ordivergent. Evaluate those that are convergent.   ∫-∞...

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Q: If  f(x) = 7x2 − x3,  find f '(1) and use it to find an equation of the tangent line to the curve  y...

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Q: If (ln x)/x = -2 ln 2, must x = 1/2?Give reasons for your answers.

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Q: Evaluate the expression.

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Q: How do I find y' using the appropriate derivative rules?

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Q: For what values of a and b is the line 5x + y b tangent to the curve y ax³ when x = 2? a = b

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Q: Calculus Question

A: Maximum value= 1/9 and minimum value= -1/9  So the amplitude is:  

Q: 1. Use the properties of continuous functions to explain why f(x) =x cos(x) +1 is a continuous funct...

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Q: The solution of the differential equation y" = 2x(y')² is Select the correct answer. tan +c2 y = C1 ...

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Q: logb x is the exponent to which b must be raised to obtain x.Determine whether the statement is true...

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Q: Calculus Question

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Q: Find the derivative. y=(5√x)/(8)

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Q: If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relativ...

A: Definition:

Q: Find the average rate of change of the function over the given interval. Compare this average rate o...

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.