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- Consider a function that goes through the two points (1, 10) and (2, 23). Findthe formula for the function ifA) The function is linear (of the form y = mx + b)B)The function is quadratic (of the form y = ax^2 + bx + c), and (1,10) is the vertex of the parabola. C)The function is exponential of the form y = ae^kx16-17. Find the derivative: y = (x² – 4x + 2)(2x3 - x2 +4) A) 2x* - 36x3 +24x2 + 4x -1 B) 2x* – 32x3 + 24x2 + 4x – 16 C) 10x* – 32x3 + 24x2 + 4x – 16 D) 10x-36x3 + 24x2 + 4x 16 | 18-19. Find using product rule y = x³ In x A) x? + 3x2 In x B) 3x2Inx C) x2 D) 3xProve that sech-¹(x) = In(¹+√¹-x²) X
- Differentiate the following function. y=x(x³ +5) ³ Choose the correct setup below to differentiate the function. [x(x5 +5)³] = (x)•. J :(x5 + 5)³) + ((x³ +5)³).) dx d « (x5 + 5)³] = « - -(x* + 5) ³) - ((x³ +5)³).) dx dx [x (x* +5)³]=2• [x(x° +5) ³].[x (x* + 5) ³] dx dx d d Ix(x5 +5)³]= x) • 3 (a5 +5) + ((x³ +5) ³) · x) d [x (x5 + 5)³] = (x) • ) + ( (x5 + 5) ³) • -c() + ( (x5 +5) ³) • (x5 + 5) ³) dx dx dx d [x(x* + 5)³ : dx(a) Write the linear interpolation/ shape functions relevant for the 2D rectangular element shown below identifying the shape function for each node. Use the property that N,(x,)= 5, to derive the functions. For example, at node 1, N = 1, so using the equations of line 23 and line 34, we (x-a)(y-b) may write N = Sımilarly, interpolation function N2 should involve equations of %3D 4ab lines 34 and 14, and so on6) What is the domain of the cosecant function?