5. For what values of x will the function, f(x) = a) -6,0 b) -6, -3,0 x-3 x³+3x²-18x be discontinuous? c) -6, 0, 3 d) -3, 0, 6

Q: 2. Determine the points on the curve f(x) = sinx-cosx, 0≤x≤27 where the tangent line is horizontal.

A: Find out the points where the tangent line is horizontal.

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A: We have to solve a part 6 and 7.

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Q: 6. Find the general solution of the PDE. The solution u is a function of x and y. Ux=x-yz +y³

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Q: Find dz/dt where z = 2xy - x² y² and x = 2t, y = t².

A: Given: Now,        z=2xy-x2y2  =22tt2-2t2t22  =4t3-4t6

Q: 18 [™ f(z)dz where a = 11 - F f(x)dr = [² (² and b 0 f(x)dr

A:

Q: 12) The growth rate for a 24-hour period of a bacteria colony is measured to be r(t) = 96e 0.24t…

A: We are allow to solve question at a time .If you need rest of answer please upload separately  Thank…

Q: 1. a) Given the lines L₁ : 7 = (1,2,−4) + t(k+ 1,3k + 1, k − 3) and L₂: x=2-3s, y = 1-10s, z = 3-5s,…

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Q: Below is the graph of y=e*. Transform it to make the graph of y=-e* +5. Give the domain and range of…

A: Given problem:- Graph of y = ex   Transform it to make the graph of y = - ex + 5   Give the domain…

Q: 4. With the fact of 1² +2²+...+ n² = n(n+1)(2n + 1)/6, prove that n n n(n −1) ΣΣ(i-j)² 6 i=1 j=1…

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Q: 4. Consider the lines 4: x=1+3ty=2+3t,z=3-10 and 1₂: a) Find the point of intersection of 1 and 2₂.…

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Q: find the slope of the tangent line to the graph of the following function at the given point fx…

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Q: 3)Evaluate the following integral by using Trigonometric Substitutions Method. dx √√9x² +9

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Q: 4 10 c) f x ¹0 (5-)10 dx x

A: Find out the integration.

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A: Given

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Q: 1 1+6402 anges JP

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Q: 1 dx 6- cos²xsin²x

A: use trigonometric identity to prove the integral

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A: I am attaching image so that you understand each and every step.

Q: Use Newton's method to approximate a root of the equation 4 sin(x) = x as follows. Let ₁ 2 be the…

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Q: 28. Which pair of lines are parallel? a. x+7y-2=0, 7=(2,5) + s(1,7), s € R b. 3x-4y-2=0, 7 = (1,4) +…

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Q: A fair coin is flipped 5 times. What is the probability of: a. Getting HTHTH, in that order? b.…

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A:

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Q: 24) Find dy /dx for the following functions : a) y². cotx= [sin(x,y)]-¹ b) y = (lnx + x) tan x

A: Given: a)y2·cotx=sinxy-1b)y=lnx+xtanx

Q: At what points of R² is the following function continuous? xy if (x,y) = (0,0) f(x,y) = 5x + 4y 0 if…

A: This is problem of limit and continuity. Based on the general formulas and concepts we will answer…

Q: By using the differential operator D and it's inverse, solve this equation: y"" - y" - 6y' = ex ex…

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Q: The diagram below is a portion of a graph of a differentiable function f(x). In this graph, which of…

A: Given.

Q: 3 B 3! - What is the second derivative of the function f(x) = xex ?

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Q: a) Evaluate the following indefinite integral of a rational function: √9-4x² dx X

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Q: Q3)Evaluate the following integral by using Trigonometric Substitutions Method. dx = √√√9x² +9 y =

A: Let's solve integration by using trigonometric substitution.

Q: For each function, determine whether it is a polynomial function. Function (a) v(x)=3x² +0.6x4 (b)…

A: polynomial can have constants (like 4), variables (like x or y) and exponents (like the 2 in y2),…

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Q: A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t=0,…

A: A tank initially holds 80 gal of a brine solution containing 18 lb of salt per gallon. At t=0,…

Q: Evaluate the following integral by using Odd and Even Powers Method: y = [₁ cos5 (1x) dx

A: We will evaluate the given integral by using odd and even power method in the following step.

Q: general solution of the differential equation y-14y+49y"=0.

A:

Q: 1. For the curve given by R(t) = (cost + tsin t)i + (sin t − t cost)j + (t^2)k, find a. the length…

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)…

A: The given function:fx=e5xWe need to find the Taylor series centered at 0.

Q: Q4) Find dy /dx for the following functions : a) y².cotx = [sin(x.y)]-¹ b) y = (In x + x) tan x

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Q: Q5) Evaluate the following integral by using Partial Fractions Method 2x²-3x+2 y = dx -

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Q: 4) √₂° e¯*dx = 5) S- dx = 4x+5 x²+x-2

A: Given, ∫2∞ e-xdxLet I=∫2∞ e-xdxI=e-x-12∞I=-1ex2∞I=-1e∞--1e2I=-1∞--1e2I=0--1e2I=1e2Therefore∫2∞…

Q: Taylor Series Approximation Formula f" f"" (a) ² f(x) = f(a) + f'(a)(x − a) + ¹¹¹(a) (x − a)² +…

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Q: Q1// Converting r= 12 cos 0 r = 12 cos 0 from polar to the equation of a circle?

A: Given problem:- Converting r = 12cos(θ) from polar to the equation of a circle?

Q: One of the following is a general solution of the homogeneous differential equation y" - y' - 2y = 0…

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