If r(t) = < ln t, ecos t, t2 >, then unit tangent is a _______ , principal unit normal is a  ____ , and its curvature is a  ____. VECTOR,SCALAR

Q: Water is poured into a conical container at the rate of 10cm³/sec. The cone points directly down, an...

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Q: y? 1. 2. Consider the equation In ry (i) Show that (r, y) = (1,1) is a solution to this equation. dy...

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Q: Question

A: We will find the value of sin theta. 

Q: 2 x y ey + y² e*v° +1) dæ + (æ² e**v +2 x y e" ° – 2 y) dy = 0

A: We have to solve given differential equation.

Q: Find the value or values of x for which the curve of the following functions has a point of inflecti...

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Q: csc 0 tan 0 dr – (r csc 0 + tan² 0) d0 = 0 -

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Q: Since lim k→+0 (k + 1)!/3k+1 k!/3* k+1 lim k→+∞ 3 +00, k! the series (converges/diverges/inconclusiv...

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Q: If f(x, y) = x cos y + ye", find dydx

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Q: ax²ª (x2a+1)°dx

A: Given,           ∫ax2ax2a+13xdx

Q: Find the inflection points of each of the given curve.  y = x3 – 3x2 + 4

A: ⊙a function y=f(x) is said to have inflection point at x=a, if its second derivative i.e. d2ydx2 cha...

Q: Evaluate the following integrals: 1. fx² ln x dx

A: As per our guidelines we are supposed to answer only one question.kindly repost others question as a...

Q: Evaluate f tan²xsec*xdx using trigonometric integrals

A: Our Aim is to evaluate the integral given below:-∫tan2 (x) sec4 (x) dx -(i)

Q: use Substitution method to schve (3メ -2Y +1)dx -(X-2Y-3)dy=o

A: We have to solve it by substitution method. 

Q: dy at the given point. dx Calculate – T T sin² (-5y) = x + y. (2) 4 4 (Give an exact answer. Use sym...

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Q: just answer p2(x), p3(x), and p4(x). and please box your answer and make it clear. thank you

A: This is a problem related to derivative of the function. Maclaurin series is nothing but Taylor seri...

Q: 42. Using the method of undetermined coefficients, write the form of the assumed particular solution...

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Q: 8x+1 Evaluate f dx using algebraic substitution V4x-3

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Q: R has degree 4 and zeros 3 − 5i and 3, with 3 a zero of multiplicity 2.

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Q: 3. Let A C B. Which of the following statements is/are true? a. AnB CA b. AUB CB c. A\B is a singlet...

A: Topic  -   set and subset 

Q: (2 x* y? + 4x² y + 2 x y² + xy* + 2 y) dx +2 (y³ + x² y + x) dy = 0

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Q: ydx+(2x+3y)dy=0 solve by using homogeneous equaations

A: We know,∫dxx=ln(x)   Given differential equation, ydx+(2x+3y)dy=0 ⇒dydx=-y2x+3y....(i)  

Q: Find the derivative of: y=x^(7sin(x)). (x>0).

A: Multiplication rule of derivative is used.

Q: A tank in the shape of an inverted right circular cone is full of water. The water weighs 62.4 pound...

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Q: (MULTIPLE CHOICE) Which of the following equations is(are) exact? (A) (x - y3 +y sin z)dr (3ry? + 2y...

A: Given problem:-

Q: What is the y-intercept of the function y = cot I? || ㅇ(T,0) O (0,0) O (1,0) (0, 1) O It does not ha...

A: The function is given as y=cot(x) The objective is to find the y-intercept.

Q: cos(2x) -dx sinx+cosx

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Q: Given the data table Years U.S. Population (millions) after 2000 1 285.5 295.5 8. 303 10 0. Use the ...

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Q: da (cos ( 3x) sin( 2æ)) dæ

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Q: Evaluate

A: Please refer to the image below

Q: Determine whether each of the following functions is (a) continuous (b) differentiable 2. f(x) = Vx ...

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Q: Evaluate f w?sin(10w)dw using integration by parts W

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Q: Which of the following is the general solution to the differential equation y?dx = (xy – x²)dy? x In...

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Q: 43. Using the method of undetermined coefficients, write the form of the assumed particular solution...

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Q: Let sk En(0.1)" n=1 Find s9.

A: Given that sk=∑ n=1k n (0.1)n -(i) Our Aim is to find s9=?

Q: d. lim f(x) e. lim f(x) c. lim f(x)

A: d.limx→2+f(x)= ?f(x)=2x ; x≥2limx→2+f(x)=limx→2+ 2x=2×2=4limx→2+f(x) =4e.limx→2-f(x) =?f(x)= x ; 1≤x...

Q: INTEGRAL Evaluate the following: 8. Se2×dx

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Q: Use the given graph of the function to find the z-values for which f is not differentiable. 1.A Answ...

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Q: Determine the approximate root (x_r2) of the f(x) = 0.35x^4+2x^3 -x^2+0.36x +4, upto 2 iterations us...

A: f(x) = 0.35 x4 + 2x3- x2 + 0.36 x +4 f(-2) = -9.68 &lt; 0 f(0) = 4&gt;0 Hence, a root lies between -...

Q: Problem 1. Draw a direction field for the given differential equation. By hand, sketch an approxi- m...

A: Solutionn is here

Q: 46. Let the assumed particular solution for the given DE be y, = (Ar³ + Bx² + Cx)e* + E. What is the...

A: A detailed solution is given below.

Q: Use geometry (not Riemann sums) to compute the integral. dx 3 Enter a pumber

A: The given integral is  ∫12 x3dx

Q: 1. x cot2 xdx X CO

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Q: A population starts with 1600 members and increases with a relative growth rate of 17.2% per year. W...

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Q: Problems: 1. Engineers have observed that when transferring a message I (an input signal) through a ...

A: All parts of the problem are solved below in detail.

Q: Let z = 6exv , find dz %3D

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Q: A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 8 ft above the bo...

A: Note: Since you have asked part b, we will solve only part b. 

Q: Evaluate the limit lim, 5 a. 2 b. 0 C -1 x d. I

A: Given: limx→5 x+11x-1

Q: 12

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Q: For the next six questions, consider the differential equation: y" + 4y = g(x), g(x) # 0

A: Let's find. 

Q: 3 V1+x3 -dx x-2

A: Given:      ∫1+x33x-2dx      =∫x2 x3+13dx substitute u=x3+1                 dudx=3x2→dx=13x2du