As in Section 1.4 of the textbook, the step function H(t) is defined by { H(t) = 0, t < 0, 1, t≥ 0. 9. Sketch the graphs of the following combinations of step functions: (a) H(t) – H(t – 3) (b) 2H (t − 1) + 4H (t − 3)

Q: Graph the Heaviside function 2(H (t+4) – H (t-1)) + (H(t-3) –H(t-6))

A: The Heaviside function is very significant in studying real valued function. The range of Heaviside…

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A: In this question, we need to find the singular point and then check these are regular or irregular.

Q: Given the function () below, decompose A(z) into component functions f(x) and g(x) so that A(z) —…

A: We can answer both the question in the below steps.

Q: 1. Find the linearization of the given function at the given point.

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Q: a) f(x)=−3x b) f(x)=3x+1 c) f(x)=3x d) f(x)=x3 e) f(x)=3−x

A: Consider the equation

Q: 1. Sketch the graphs of the following combinations of step functions: (a) H(t)- H(t-3) (b) 2H(t-1) +…

A: Sol

Q: 6. Consider the transformed function g(x)=-3| () +2 of the function f(x)= -(3)', Find the horizontal…

A: We have given function  gx=-315x+2 Horizontal intercept occur when g(x) =0 Put gx=0 -315x+2=0…

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Q: so if|x| 2 43. f(x)

A: Following is the graph plotted for individual functions.

Q: Example 1.7.1. Given the function g(x) = 2x2 + 3x – 2, find g(5) %3D

A: Given  g(x)= 2x2+3x-2 We replace x by 5 in above to get g(5)

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A: We have to find the value of f'(3)We using the formula of divided differentiation.

Q: F(x)= G(x)= (Fog)(x)= (Gof)(x)=

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Q: f(x) = 2x² - 4x + 7.

A: Fundamental Principal of Derivate for f(x) is limh→0f(x+h)-f(x)h

Q: I need help with the graphing part

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Q: (a) Sketch the graph of the given function. -{; 2, f (t) = 0<t < 2 2e-(t-2) f(t) 5| 4 3 2 2 3 (b)…

A: Given : f(t) =2,0≤t&lt;22e-(t-2)t≥2

Q: 1. Sketch the graph of f(x) = -x²(2x + 5)*(x – 3)4.

A: Given f(x)=-x2 (2x+5)3 (x-3)4

Q: (a) Develop f (x – 4h), f (x + 3h), ƒ (x) and ƒ (x+ 4h). a first-order method for approximating f"…

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Q: 2. y 1 8 10 shows the graph of the function f (x) =

A: Let's find.

Q: Example 4.3.4. Consider the function h(p) = (e2-P) (3P - p²) (a) Locate any extreme values of the…

A: Given Function: hp=e2-p3p-p2 To Locate: Any extreme values of the function on the interval -1≤x≤4,…

Q: f (x) || 2x+5 5x-1

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Q: (a) The graph of f(x) = (x + 42) can be obtained from shifting the graph of f(z) = to the %3D 42…

A: here we have graphical transformations.

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Q: (a) Are the following functions surjective? Justify your answers. (i) The function a : Z→ Z defined…

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Q: %3D If a (z) = x+1, b (x) = x- 2, c(x) = x + 3, d(x) = x – 4 | a (b (c (d (5)))) %3D

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Q: Sketch a graph of f(x) (2x - 1 if x 2

A: To sketch the graph f(x) ={  2x-1 if x&lt;2               x-2  if x&gt;=2 for x&lt;2, y=2x-1…

Q: Consider the function defined by f(x) = −x³ + 6x² - 10. (a) Determine the values of x for which f(x)…

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Q: 8) f(x) = 5 - 20 18 16 14 12

A: The graph is shown in step 2