A curve joining the points Pı and P2 in R² is parameterized by two different paths,7(t); t1 0. Assume that 7, B, and h are all C1.(a) Prove that•t2T217()|| dt = " 13(-)|| dr.t1T1(b) Interpret the result geometrically.

Given: →γ(t);t1≤t≤t2→(τ);τ1≤τ≤τ2β To find: a) Prove that ∫t1t2→γ'(t)dt=∫τ1τ2→β'(τ)dτ. b)…

Answered: A curve joining the points Pi and P2 in…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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o'pg. 156-159 J #1.) Determine f' and F", if (x)=x²-14 X4 #2.) For y = x9-7x³ +2, find d²y dx2 #6) Determine the maximum and a f(x) = 2x³-9x², -2≤ x ≤ 4 minimum of each function on the given interval b) f(x) = 12x - x³, x= [-3,5] (²) f(x) = 2x + 18,1 fcx)=x²-2x + 6₁-1 ≤ x ≤7 b) f(x)= x³ + x², -3 ≤ x ≤ 3 Cf(x)= x³-12x + 2,-5 ≤ x ≤ 5 d.) f(x) = 3x5-5x³, -2≤x≤4
Ofx)=5x"_3x²-Z+t] 4 2 find f6 and fW) (x) f =x* Inx find f') and fe
1) In this problem, let x = 2, the value Ax = dx, dy = f'(x)dx, and Ay = f(x + Ax)-f(x) to complete the table f(x)=√x 1.0000 0.5000 0.1000 0.0100 0.0010 2) dx= Ax dy Ay Ay - dy dy Ay 3) 4) f(x) = 5x √2x+3 Find the first derivative given that dy Find X by implicit differentiation. √√x+y+√√x = 4 dx -лr² h A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at the rate of 10 cubic feet per minute, find the rate of change of the depth of the water the instant it is 8 feet deep? 1 V
Determine whether the given set of functions is linearly independent on the interval (-, ). fi(x) = 3, f2(x) = cos²(x), f3(x) = sin? (x)
Ex. 5) For R and Q functions and given that: Q(-1) = 5, R(-1) = -4, R(5) = 7; || Q'(-1) =-3, R'(-1) =2, R'(5) =-1 If f(x) = R(Q(x)), then evaluate f"(-1). f"(-1)=
Let f(x) = In[x6(x + 4)5(x² + 6)⁹]. Find ƒ'(x). f'(x) =
Let F(x) = f(x³) and G(x) = (ƒ(x))⁹ . You also know that a³ = 2, f(a) = 2, ƒ'(a) = 5, and fƒ'(aº) = 9. Find F'(a): and G'(a) = - = ← ID
Consider the three points (2, 2), (4,4), and (6, —2). (a) Supposed that at (2, 2), we know that fx = fy = 0 and ƒxx 0, function near the point (4,4)? ? fxy fry = 0. What can we conclude about the behavior of this (c) Supposed that at (6, -2), we know that fx = fy = 0 and fxx > 0, fyy < 0, and fxy = 0. What can we conclude about the behavior of this function near the point (6, -2)? ? Using this information, on a separate sheet of paper sketch a possible contour diagram for f.

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A curve joining the points Pi and P2 in R2 is parameterized by two different paths, 7(t); t1 0. Assume that 7, B, and h are all C1. (a) Prove that t2 T2 7()|| dt = I }(+)|| dr. (b) Interpret the result geometrically.