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Use the linear approximation of f(x) = sin(5x) at x = 0 to approximate sin(3). 15...
8pt (4. Let f(x) = 4+0+ sin a. (a) Find the linear approximation L(x) of (a) at a = 0. reo)= (4+0+0= dusa (0) +csx) : ' +wJy -' *wslo), ? zru txtsinx ? Ju+x-sior ? Surotu u TPH (b) Use the linear approximation from part (a) to estimate (06) 0.5 0.06 30 2 + 1 (x-6.06) 2 + 1 x .03 - 2 (x+1896 pt ) 0.030
parta- Use linear approximation, i.e. the tangent line, to approximate as follows:Let f(x) = x 6. The equation of the tangent line to f(x) at x = 2 can be written in the form y = mx+b where is: and where is: Using this, we find our approximation for 1.86is Box 1: Enter your answer as a number (like 5, -3, 2.2) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity Box...
1) 2) 3) Use linear approximation, i.e. the tangent line, to approximate 15.22 as follows: Let f(x) = z² and find the equation of the tangent line to f(x) at x = 15. Using this, find your approximation for 15.22 Given the function below f(x) = -180x3 + 396 1. Answer in mx + b form. Find the equation of the tangent line to the graph of the function at x = L(2) Use the tangent line to approximate f(1.1)....
(1 point) Use linear approximation to approximate 36.4 as follows. Let f(x) = x. The equation of the tangent line to f(2) at x = 36 can be written in the form y = mx + b. Compute m and b. m = b= Using this find the approximation for 36.4. Answer:
7. Find the linear approximation of the function f(x,y) = ery at (1,0) and use it to approximate f(0.9.0.1). (6 Pts)
(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...
Let y = sin(4x). If Ax = 0.3 at x = 0, use linear approximation to estimate Ay Ay = = Preview Find the percentage error rounded to 1 decimal place. error = Preview
7. (5 points) Find the linear approximation for f(x) = tan(2x) at a = 0 and use it to approximate the value of tan(0.002). Hint: The linear approximation is just the tangent line to the curve at a = 2. 8. (5 points) Use the Mean Value Theorem for derivatives to find the value of x = c for f(x) = Vx on the interval (1,9). 9. (5 points) The acceleration of an object moving along the number line at...
(1 point) Use linear approximation, i.e. the tangent line, to approximate 15.3 as follows: Letf(x) = x2 and find the equation of the tangent line tof(x) at x = 15 . Using this, find your approximation for 15.32 (1 point) Use linear approximation, i.e. the tangent line, to approximate 15.3 as follows: Letf(x) = x2 and find the equation of the tangent line tof(x) at x = 15 . Using this, find your approximation for 15.32
(3.2) Consider the data given in the following table 05 1 15 f(x) 0 2 0 6 1 2 20 (4) (a) Approximate f with a function of the form q (x) = kxm (4) (b) Approximate f with a function of the form g2(x) = be Which approximation between q and g2 1s more appropriate for the given data? Justify your (3) (c) answer < In, and a piecewise cubic polynomial Consider a set of points (I,) Such that...