00 00 If 0 < f(x) < g(x) for all r and | f(x)dr diverges, g(x)dx diverges. then

Q: (2x+1 x² +2 x> h) Xsh Q3) If the function f(x) %3D having limit at x h. Find the value of h.

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Q: 5x The interval over which the function f(x)= e (1+x) becomes continuous is O [-1, 0) O (-0,…

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Q: 00 Suppose 0 < f(x)< g(x) and both are continuous on [a, o0). If | 9(x) dæ diverges, 00 | f(x) dx.…

A: We have to apply the comparison test

Q: Proof the n + 1 derivative of xk is zero, where k <n

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Q: 3x-1 ind the critical points of the function f (x) = x+6

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Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

A: Consider the given statement "If f is a continuous at x = c, then f has a derivative at x = c".

Q: Use the graph of the first derivative function f'(x) to find x values at which function has relative…

A: First of all, consider the graph of f '(x).

Q: If f(x) is an even, continuous function for which = 4 and dx = 4, then f (x) dx 3 2

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Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: f(x)=e^-5x at x=0

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Q: 1 - t Let F(x) = dt for -o << x < +∞ t2 + 24

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Q: a) Find the critical value(s) of f(x) = x + 2sin(x) on the interval 0sxs 27

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Q: f(x)dx converges then lim,f(x)=0

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Q: 4 – x² p(x) = x – 1 at x = 0 Select the correct response: Continuous O Discontinuous

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Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

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Q: (c) A non-constant function f : [0, 1] → R such that f(x) > 0 for any r e [0, 1] but | f(x)dx = 0.…

A: Let us consider a function f:0,1→ℝ such that fx≥0 for all  x∈0,1.  Suppose fxn be a sequence of…

Q: 3. f(x) = Vx - 5 is continuous on the interval [5, 0) %3D

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Q: -2 x< -1 Q1)a) For what values of a and b is g(x) = ах — b -1<x<1, x21 Continuous at x= -1

A: The suitable formula for continious       LEFT HAND LIMIT = RIGHT HAND LIMIT

Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: V4+x-2 If f(x) = ,x*0 be continuous at x = 0, then f(0) = 1/2 1/4 3/2

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Q: -x if x 0 1 if a 0 f(x) and g(x) both f and g are continuous at 0 fg is continuous at 0 fg is…

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Q: (c) Let g : R → R be a continuous function such that +5x-9 g(t) dt = –3x . Help Willow find the…

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Q: function f(x) such that f'(x) = (2x – 1)e²“. O Find the interval/s on which ƒ is increasing /…

A: Explanation: Given that,                          find the critical points to put the f'(x) = 0…

Q: • Find f (x) of f(x)= by using the definition of the x-1 derivative. • 1- Find if y=3t-4 and t Vx+…

A: we have to find the derivative using definition. as per definition  f'(x)=limh→0f(x+h)-f(x)h

Q: Ax) = xin( ) given function calculate taylor poynomial of f(x) of degree 4 at a=4

A: Solve the following

Q: lim f(k+h)+f(k) h→0 ds Q3) Using the definition calculate the derivatives h dk 1 S= k – k of the…

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Q: A continuous function y = ƒ(x) is known to be negative at x = 0 and positive at x = 1. Why does the…

A: Given that f(0)&lt;0 and f(1)&gt;0  f(x) is a continuous function.

Q: lim f (x) = 4 f(x) has a HA at y=4 418 O True O False

A: From the given problem: limx→∞fx=4 As we know that; To calculate the horizontal asymptotes, solve…

Q: 2 2x +1 Let f(x) =- |- log, (x² + + 1) • (b* - 5b +3)x +c. If f(x)isa tan decreasing function of x…

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Q: 8. Find the derivative of the f(x) = ntan x at x = " А. п B. 2 In(1) C. π In (π) D. 2 n In() E. 2n…

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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,…

A: Our objective is to solve the above questions.

Q: True or False Suppose f is differentiable everywhere. Then the chain rule assures that d/dxf(f(x)) =…

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Q: Ax) = xin() given function calculate taylor poynomial of f(x) of degree 4 at a=4

A: solve the following, since previous question is not given so i can't evaluate error

Q: 2 The function f(x)= (x² – 1) ³ , is decreasing on the interval (- 00,-2)U (0,2) AO (-1,0) U (1, ∞ )…

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Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b -1<x<1, 3 x21 Continuous at x=0

A: F is continuous at any point then left hand limit is equal to right hand limit. if limit is not…

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: To determine the linearization for the function.

Q: S x2 – 3 |kV5+x _if x > –1 if x < -1 - 2. Determine the constant k such that the function f(x) : is…

A: As per our guidelines, I can answer one question and maximum three subparts of a question. Since you…

Q: Find the linearization at x = a. f(x) = sin3 (x), a = 4 (Use symbolic notation and fractions where…

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Q: b) Let f(x) = ¹. Find f'(x), ƒ"(x), ƒ"(x) and ƒ(4) (x). Deduce f(n)(x).

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Q: 4. Find the local maximum and minimum values of f,using both the First and the Second Derivative…

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Q: 5. Find the linearization L(x) of f at a = 0 f(x) = = 1 = 0 2+x

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Q: Using the graph above, state where f (x ) (a) has critical points: (b) is increasing: (c) is…

A: According to the given graph: (a).   f(x) has critical points at:  x=0,   x=4   and   x=7

Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x* + 5x…

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Q: 5x−12/x^2−x−42 has vertical asymptote(s) at x=

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Q: 32 Find the linearization L(x) of f(x) = ÷- at x = 4. 12

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Q: 2x+1 tan" log, (x +x+1)+(b-Sb+3)x+c. If f(x) is a -1 Q: Let f(x)= V3 decreasing function of x for…

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