3. Assuming that the following equation defines y as a differentiable function of x, find the...
dy Find for the following equation. Assume that the equation implicitly defines y as a differentiable function of dx Vx? + + 2xy + y4 = 2.
Assuming that the equation defines x and y implicitly as differentiable functions x =f(t), y =g(t), find the slope of the curve x =f(t), y=g(t) at the given value of t. x3 +41? = 37, 2y3 - 22 = 110, t = 3 The slope of the curve at t= 3 is (Type an integer or simplified fraction.)
(a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the linear approximation for f(x) around a = e and use this to approx- dy Hence, e T,y 5 marks imate f(3). markS (b) Evaluate the following limits. Simplify your results if possible. 5 marks 5 marks] lim cot 5x sin 6x cos 7a (i) (ii) limIn (a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the...
Please help with this question. Thank you! 1. We say p (ro. yo, 20) is a regular point for the equation F(x, y,) 0 if the equation either defines as a differentiable function f( for (, y) in a neighborhood of (ro, Vo), or defines y as a differentiable function y-g(, a) for (r, z) in a neighborhood of (ro, 2o), or defines z as a differentiable functionh(x, y) for (x, y) in a neighborhood of (ro.o). a. Suppose p...
ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A. dx 8 X xf (x) 7f(x) dy O B. dx 8 X dy xf(x) 7f(x) O C. dx 8 X 7f'(x) xf(x) dy O D. dx 8 X ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A....
Given the equation y In (x + y + 8) = 3, evaluate Assume that the equation implicitly defines y as a differentiable function of x.
Assume that x and y are both differentiable functions of t and are related by the equation 42 y= 22 +3 Find dy when 2 = 0, given dt de dt 2 when x = 0 Enter the exact answer. 11 dt
true or false is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
oft Let's X and Y are both differentiable danction Find dx when (x,y) is (4,3), and dy dt for the equation xty² =25
find the function y=y(x) for x>0 which satisfies the seperable differential equation, dy/dx=(4+17x)/(xy^2), x>0, y(1)=3