Q1:/ Find the general solution of non-homogenous differential equation using Variation of Parameters method y" - y' = e* cosx

Q: f(x) = In(x4 + 1)

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Q: 12. Find an equation for the tangent plane to the surface given by 2xy = 2z2 - ryz at the point…

A: Use tangent plane formula

Q: Indicate whether the following statement is true or false. P(x) Let P (x) and Q (x) be polynomials…

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Q: Use the Binomial Theorem to write the expansion of the expression. (r + 3s)3

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Q: Sketch the region enclosed by x + y? x + y = 0. = 12 and = 0. a) Favoring convenience, should you…

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Q: x3 dx J4- x4

A: ∫x3dx4-9x4Multiply & divide by -36 =-136∫-36x3dx4-9x4since, ∫f'(x)f(x)dx= 2f(x)

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: If f is continuous at a number, x, then f is differentiable at x. True

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Q: Let Sx² + 3 f(x) = l(x - 2)2 if x 2 1° if x < 1 (a) Find the following limits. (If an answer does…

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Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

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Q: Given the following functions: f(x) = cos(x) g(x) = x7 + 1 d d Find f(g(x)) and g(f(x)). (Use…

A: Given the following functions: fx=cosxgx=x17+1To find ddxfgx and ddxgfx.

Q: The growth rate in the weight w(t) in kg of a Persian cat can be represented by w'(t) = 6e-0.25t,…

A: Here we have to use the concept of integration for solving the given problem.

Q: Find the volume of the solid that results when the shaded region is 6 revolved about the indicated…

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Q: 4. Show that a b a +

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Q: I z x sin(y²)d.xdy Calculate

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Q: 2. Solve the following initial Condition Problems: dy а. dx Vry, y(1) = 2. || b. y' = x + y, y(0) =…

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Q: In exercises 9–14, find all critical numbers and use the Second Derivative Test to determine all…

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Q: Find the faur fourth root of (-16)

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Q: A: By using Linear equation solve the first order differential еquation y' + sec(x)y = cos(x)

A: The given differential equation is;  y'+sec(x)y=cos(x).

Q: Find the derivative of the function y 6 tan-' (). %3D (Use symbolic notation and fractions where…

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Q: Use the formula k(t) : ||r() × r"(t)|| to find K(t). %3D r(t) = t²i + t®j %3D

A: Given that,     r(t)=t2i+t9j

Q: Compute f(x)dx (6 points) f(x) = { 2x if x<1 4 if x21

A: In this we have to do the integral of given function so I'm providing hand written solution for this

Q: Prove that f : [−4,2] → R defined by f(x) = 7/x+5 is uniformly continuous on the interval [−4, 2]…

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Q: Find the average value of the function f(x,y)=y2√x +5 over the rectangular region R=[2,4]×[3,4].

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Q: f(u) = u + u g(x) = cos (x) Find the following function and derivatives. (Express numbers in exact…

A: We have to find out function

Q: Use the dotted line as your y-axis and the solid gray line as the x-axis. Find the distance from the…

A: We need to find area.

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. da dz dy = y -54 J-36 %3D

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Q: The Leslie matrix below describes a population with four age groups consisting of juveniles,…

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Q: 00 dz Either show that the improper integral converges and find its value, or show that it diverges…

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Q: Find the exponential function that contains the points (2,48) and (3,192).

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: As we know that; The critical number of the function, y=gy can be determined by solve the equation…

Q: Find the length of the curve of the graph of the indicated function. y = (x + 3)3/2, between points…

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Q: The slope of a curve at any point (x,y) is given by dy/dx= 8 - x.  If (2,14) lies on the curve, find…

A: find the equation of the curve.

Q: 254. The sides of an equilateral triangle is increasing at rate of 10 cm/min. What is the length of…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: The International Space Station orbits the Earth at a height of 250 miles. What is the height of the…

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Q: 15. ſ sin² 3t cos 3t dt

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Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: Show that the lines L1 : x =1- t, y = 2t, z = 4+t and L2 : x = 1+ 3t, y = 3 – 6t, z = 5 – 3t are…

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Q: 31 What is the volume of this cylinder? 6 m 7 m Figure not drawn to scale Use T 3.14 and round your…

A: Given :Diameter of cylinder= 6 mHight of cylinder = 7 m

Q: Given the following functions: f(x) = cos(x) 17 g(x) : = X + 1 Find f(g(x)) and (f(x)). (Use…

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Q: Evaluate the integral by choosing a convenient order of integration: x cos(ry) cos (Tx) dA; R= x (0,…

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Q: f(In) For the function f(x) = x + 3x + 1, write Newton's formula as En +1 = F(In) = In - %3D for…

A: Topic:- application of derivatives

Q: Set up the definite integral required to find the area of the region between the graph of y = – 23x…

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Q: k lim (1+†) k→∞ k

A: We have to find limit

Q: dz (е) dz

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Q: Find the linear approximation at x = 0 to each of f(x) = (x + 1)², g(x) =1+ sin(2x) and h(x) = e2*.…

A: To find the linear approximation at x=0 to the given functions using the formula:…

Q: Cos 4x S cos 2x-sin 2x dx

A: This is a problem related to integration. Based on the general formula and concepts we will answer…

Q: dx In x +1+ Vx² + 2x| + C Vx2 + 2x

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Q: pproximate using differentation:  e0.99 Please show step by step solution.

A: This question can be solved using the concept of approximation using derivatives.

Q: e-* dædy by changing the limits of integration appropriately. y/2 20. Evaluate

A: To evaluate the value of double integral.