5. If f(x) = 5, which of the following represents f '(3)? 5. lim Ar a. 5-5 lim Ar Ar 0 е. Ar 0 b. 3 3. lim Ar line f. Ar0 5-3 lim C. Ar 0 Ar g. Does not exist d. h. None of the above

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Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

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Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

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Q: 4 Suppose that f(1) = 9, f(4) = -7, f'(1) = 6, f'(4) = -1, and f" is continuous. Find the value of…

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Q: The slope of the tangent line to the graph of the function y=3V-4at (16,8) is 16.00 4. -1.00 O-0.50…

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Q: 3 B Consider the following function, z= x -2xyty't yn Lind the alues of ag Ddz,z,when redgyel dy 6.

A: Given : z = x2 -2xy + y3 + yw

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Q: S 1/x ifsxs1 n*x if 0sx< Given fn : [0, 1] → R, defined as f,(x) = then the point wise limit of…

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Q: Prove: ex. a. ſ csch x = In b. S sech x = 2 Arctan(e*) + c

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Q: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of f(4)?

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Q: If f(x) = In(tanh(2x)), then f' (x) is Select one: a. -2 coth(2x)sech (2x) :): b. – coth(2x)sech (2x…

A: f(x)=ln(tanh(2x))f'(x)= 1tanh(2x) ddxtanh(2x)we know that  tanhx=ex-e-xex+ e-x…

Q: Given the function f(x) = x² – 2x, what is equation of the tangent line to the graph of f at x = -1?…

A: 1. f(x)=x2-2x at x=-12. f(x) and g(x) are differentiable functions, f'(x)=3x and g'(x)=2x23.…

Q: 4). If f(1) = 12 and f' is continuous and f'(x) dx=17, what is the value of f(4)?

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Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

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Q: 2. The solution of the following equation is equal to: * iz'+1 lim +1 1 O 3/2 the limit does not…

A: Limits Definition: A function w=fz is said to have the limit l as z tends to z0 if given ε&gt;0…

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Q: Suppose that f is a differentiable function with f(2) = 5 and f'(2) = 7. Let h(x) = f(e*). Find an…

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Q: 5. If f (2) = 5 for the continuous function f (x), calculate the following limit value | F(t) dt lim…

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Q: 4) If y = (x² + 1)cos(3x), then find dy/dx. 5) Evaluate the following limit e cosx – 1 lim x-n/2 2x…

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Q: Q3) If the function (2x + 1 +2 x > h) XSh f(x) having limit at x = h. Find the value of h. Q4) f(x,…

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Q: 1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.

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Q: Q2: Evaluate: 2 In cosy, [1] limy-o [; y4

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Q: '18 6. If f is continuous and f(x) dx = 16, find f(2x) dx. %3D

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Q: If f(x) = x2+1 for x > or equal to 0, then is arcf(x) has a tangent at x=1

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Q: b) Use it in oonjunction with Simpson's 1/3 nule to integrate the same function for ive egmenta…

A: Introduction: Simpson's rule is a method to approximate a definite integral. The interval must be…

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Q: 5. Consider the function S 2r – 1, si x < 2 f(x) = 6-x, si x 2 2. The Limit x 2 f(x) is:

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Q: 7. Suppose that the function f (x)=2-sin(e*) is continuous on with equal step 2'2 size, h equal to .…

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Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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Q: 4 '2 If f is continuous and f(x) dx = 10, find | F(2x) dx. %3D

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Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.