Q: Find the local maximum of f(x) = -sin2x – x defined on 2'2
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Q: Explain why the function g(x) = ln(4-x2) + square root of x+1 is continuous at every number in its…
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Q: use the second derivative test to find the local exterma of the function f(x) =x3-9x2-48x+72 on R
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Q: Find max and min of function on the interval f(x)=-x4-x3+5x2-4 on [-2,1]
A: The given function is; f(x)=-x4-x3+5x2-4 on [-2,1]
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A: fx=-2x2-3x+8; 0,4 Put x=0 into the given function. f0=-202-30+8=8 Put x=4 into the given function.…
Q: What are the zeros of f(x)=2cos(3x)+1 on the interval [0,π]?
A: We have the given function as fx=2cos3x+1. In order to find the zeros of the function fx, we must…
Q: Show that the functi on When x g 0 f(x)= +1 0 . When x = 0 is discontinuous at x = 0.
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Q: use the second derivative test to find the local exterma of the function f(x) =x3 -9x2-48x+72 on R
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Q: Find the approximate root in 5th iterations of the function f (x) = x - 4x2 + x +3 in the interval…
A: given fx=x3-4x2+x+3 find the approximation in 5th iterations of the function in the interval -2,-1…
Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…
A: Given, The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.
Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…
A: By intermediate value theorem, if fx is continuous on an interval a,b and fa≠fb, then there exist a…
Q: Find the roots of the function f(x)=(2x-1)(x2+2x-3) with x belong to R
A: f(x)=(2x-1)(x2+2x-3)=0 We have find all the real numbers that make f(x)=0 because it is given that x…
Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…
A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1
Q: 9. Use the Intermediate value theorem to show that f(x) = 2x( – 3 has a zero in the interval [1,2].
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Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.
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Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].
A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].
Q: 92. Use the definition of the derivative to prove that every quadratic function f(x) = ax² + bx +c…
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Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f(x) x - 1
A: To show the f(x) has roots between a and b we have to show that
Q: Use Taylor's polynomial of degree 2 of the function f(x) = tan 1(x+1) + x² %3D about c = - 1 to…
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Q: Assume that f is a polynomial and x = 10 is a critical number for f If f''(10) = -sqrt2 what do we…
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Q: Prove that constant function is differentiable at ever x ER.
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
Q: 5. Show that the function f (x) has roots between (0,2) x + 2x – 3 f(x) = %3D x – 1
A: Given that: f(x)=x2+2x-3x-1
Q: Show that f(x) = x – cos(x) has only 1 real zero on the interval [0, .
A: given fx=x-cosxx∈0,π2
Q: 4. In f(x) = {1– x² if -1sxs 1. Is the function continuous at x=1? Prove. (x² – 1 if x > 1
A: Given Function: f(x)={x2-1, if x<-11-x2 if -1≤x≤1x2-1 if x>1 To…
Q: Find the absolute maximum and minimum assuming the function is f(x) = 2x^4 - 8x + 3 on interval…
A: f(x)=2x4-8x+3
Q: Prove that f(x)=x^3+x-1 has a root in the interval [0,2]
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Q: Show that f(x) =12(logx+1)+x² -10x+3 is a maximum when x=2, a minimum when x=3;
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Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?
A: Suppose are continuous function at then rational function is continuous at if .
Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?
A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…
Q: Show that the nth Maclaurin polynomial of f (x) = arcsin x for n odd is 1.3 x Tn (x) = x+ 23…
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Q: what is the value of x in second iteration of the function f(x) = sinx - X +5, in the interval of…
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Q: 6. Obtain the TSE of f(x)=2x-² in powers of (x-1).
A: Solution is here
Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…
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Q: What is the domain of g(x)=ln(25x-x^2) Show all the work.
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Q: Find local maximum or local minimum of f (x)=sin 2x-x defined on 2 2
A: The given function is fx=sin 2x-x. Obtain the critical points as follows. Find f'x as…
Q: See image below.
A: We subtract x from both sides
Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?
A: Given: hx=7x-5,x<13x2-x,1<x≤3 We know that any given functiony=fx will be continuous at x=a…
Q: 5. Use the second derivative test to determine whether f (x) = x3 – 9x2 + 24x +5 has a local maximum…
A:
Q: Show that the f(x)=x-(In x)^{x} =0, has at least one solution in the interval [4, 5].
A: There are more than one question. We will solve the first one. Given, f(x)=x-[ln(x)]x, we need to…
Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…
A: Proceed as shown below...
Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…
A: Given function is : fx=9x2 , x≥1ax-6 , x<1 Here given that function is continuous…
Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f (x) = X - 1
A: Given that
Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…
A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…
Q: 13. Use the Intermediate Value Theorem to show that f(x) = 2x° – 3 has a zero in the interval [1,2].…
A: Given:-f(x)=2x3-3 using the intermediate value theoremf(x) is continuous in the interval 1,…
Q: Show that the equation x - 17x +c = 0 has at most one solution in the interval [-2, 2]. Let f(x) = x…
A: The given equation is : fx=x3-17x+c The given equation has at most one solution in the interval…
Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…
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Q: show that the function has neither an absolute minimumnor an absolute maximum on its natural domain.…
A: y=2x-sin2x The domain of given function is -∞, ∞. The range of sin2x is -1, 1.
Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…
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Q: Find an approximation that is accurate to three decimal places to the zero of f (x) = x³ -3x- 1 in…
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Prove that f(x)=4x-2^2x has at least one real zero in the interval [1,2] without actually solving for x.
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