Consider the function f (x) = 4e® + 7. What is the exact value of C in the interval 0, 5 such that f (c) = fave? Note: Maintain fractions if applicable. a n 8 P 8 I lim

Q: 2x+ 1 -1<r<1 1) Let , then lim f(x) 1<x<4 a- 0 b- Not exist at x=1 C- -3 d- Non a

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Q: 2t Q3. Find the value of: lim,-0 tant (x² -1 Q4 Let f(x) ={ 2kx x< 2 x 2 2 Find the value of (k)…

A: 3. to findlimt→02ttant4. to find value of k for the function to be continuousf(x)=x2-1x&lt;22kxx≥2

Q: Q3) Using the definition, lim f(k+h)+f(k) h-0 ds calculate the derivatives dk h of the function : k…

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Q: 1) Let f(x) = 3 Fx-2,x 3 a) lim f(x) b)lim Tー3 f(x) c) lim S(x) d)f(3)

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Q: If f(x) = tan(x) ,then lim %3D A) 1 B)- 2 C) 0 D) 2

A: This question is related to limit of function, we will use trignometric identities to calculate the…

Q: 1) Find the value of C that make the function continuous at x-1? x 1 -

A: We have given piecewise function  Function is continuous at x=1 if  f1+=f1=f1- f(x) = C-x        if…

Q: a. Find the value of (k) that make fhe fimction contimuous at x = 0 3k -3 =0

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Q: Find the limit algebraically. Let c and d represent arbitrary real numbers. lim Vx + cx – V |x² +dx…

A: Using method of rationalization.

Q: If f(x) is differentiable at x = 2 and lim2 x*f(2)-24 28, then f'(2) = %3D x-2 Select one: O a. -1 O…

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Q: Which of the following defines f (5) for f(t) = Va-4? a) 4 lim +5 x- 5 b) Va – 4 – 1 lim I - 5 c) Væ…

A: fx=x-4

Q: f(x) = 1 is discontinuOUs at x=2 because %3D x- 2 A. f(2) is not defined B. lim f(x) is existing C.…

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Q: f(x) 0.5 0.7 2.4 0.95 2.9 0.995 2.99 0.9995 2.999 f(x) 1.6 1.35 4.2 3.7 1.05 3.1 1.005 3.01 1.0005…

A: The given set of tables are as follows -  Using the above table we have to find the value of -  (1)…

Q: 1. Consider finding the root of f(x) =x´ – 5 use secant method, ɛ = 0, and start with the a interval…

A: given , f(x) =x2 - 5  we have to find roots of f(x) in interval by using secant method

Q: Q2/Show that the functions is harmonic u = 2 x (1 - y)

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Q: lim Σf (xf) Δx)]. V Axi→.

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Q: Q. 2 Find the following limits v' -8 a) lim v* –16 v+ 2 4x –x 2- Vx b) lim 4

A: The limit of a function is the value of the function at which the arguement for the function tends…

Q: 2) An elastic tire is described by the iven by the function f(x, y) = 4xy. Use

A: Introduction: The Lagrange methodology is employed to maximize or minimize a general performance…

Q: f(z) = 7. Use f'(x) = lim e+h-©) to find f'(x). %3D %3D 3z-7

A: The given funciton is:fx=23x-7To find f'x

Q: f(x+h)-f(z) For the function f(z) = 4x + 14x + 26, find f'(x) using the definition lim h-0 %3D O 28z…

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Q: 1. Find the discontinuity point/s of f(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…

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…

A: Now,

Q: b. Determine if the lim f(x) exists, if f(x) is defined as follows: X4 12x + 3, 5x-9, x < 4 x 24…

A: Both question are solved as, follow

Q: x2 Consider the function f(x, y) = 2y lim (x,y)(0,0) f (x,y) does not exist by using e – 8…

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Q: lim, „(Væ² + x – x)=? O a. 0 O b. 1 O c. Limit does not exist O d. 00 O e. 1/2

A: In these type of questions just rationalize the given term and simplify the fraction before finding…

Q: f is odd, J'(x) |for æ > 2, f"(x) > 0 for 0 3, lim f(x) = -2

A: First we will construct the graph for x&gt;0.  Now, point x=2 is minima and x=3 is inflection point:…

Q: I if X > 4 and J (X). 4X + 1 i1 X<4. Find lim f(x) x→4+

A: Given; f(x)=√x-1 if x&gt;4 and f(x)=x2-4x+1 if x&lt;4.

Q: Sirlw)dk= f (x) κ= lim Σ fx%) Δx 25.) Use the definition, -2x n+00 i=1 to evaluate Σ Ei=" (n+1) Eř="…

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Q: f(x) (4) lim x-c g(x) L M provided M0 and g(x) #0 for any a E

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Q: Let x²+y4 x?+4y4 f(x.y)= be given. Which of the following is TRUE for this function? lim f(x,y) =0 O…

A: on solving this we get the

Q: Use the graph of y = f(x) in the figure below to find the functional values and limits, if they…

A: This is a problem related to limit and continuity of the function. Based on the general formula and…

Q: Choose the best reason why the function f(x) = In(x – 1) is discontinuous at a = 1. A. lim,-→a f(x)…

A: Given query is to find th correct reason why f(x) is discontinuous at a= 1

Q: Find an equation of the tangent line at x = 2

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

A: Using the definition of derivative have to find  dS/dk ,where S( k ) = k + 1/k.

Q: f(x) = x³ (7) (8) is continuous for all x but not differentiable at x=0. _limf(x) may or may not…

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Q: nd the one-sided DNE lim_(x². +x+5) x--5- exists). (If an answer does not exist, enter DNE. Submit…

A: Topic:- limits

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: 1. Consider the function f(x) = (Va-1), where a> 0, a> 0. (a) Tell if f is an indeterminate form? If…

A: Solution: Given: Let the function  fx=x  ax -1  ....1 There exist a interval  a&gt;0 , x&gt;0.

Q: x*-16y* lim (x.y)¬(2,1) x2–4y2 A 0 B 00 C Does not exist D None of these

A: Topic - limit

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

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Q: f(x+h)-f(x) For f(x) = V3x + 34, find f '(x) using the definition f '(x) = lim h h0

A: Solution:differentiate by first principle

Q: f(x) 0.5 2 0.7 2.4 0.95 2.9 0.995 2.99 0.9995 2.999 f(x) 1.6 4.2 1.35 3.7 1.05 3.1 1.005 3.01 1.0005…

A: To find the limits.

Q: f (æ) = { x - cif x > 2 a² + cx – 5, if x < 2 lim f(x) determine the value of c so that r+2 exists…

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Q: Find lim f(x) for the given function and value of c. Xc* 6x 4x + 6 f(x) = C= 6 X+1 メ+プ 6x 4x + 6 lim…

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Q: c. lim d. lim f(x) = x+3, x1

A: c. limx→11x+1=11+1                   =12

Q: If     limx→3f(x)=7 ,  which of the following must be true?    I.    f   is continuous at   x=3.…

A: limx→3f(x) = 7This means thatlimx→3-f(x) =limx→3+f(x) = 7The f(x) approaches the limit value of 7,…

Q: Forf (x) = 2x +2, compute lim ƒ(1+h) –f (1) %3D f(I+h) -f (1) lim h>0 %D h

A: Given : fx = 2x+2

Q: For f(x) = find 24x dy using the definition, %3D dx dy Ay lim f(x + Ax) – f(x) = lim Ax-0 %3D dx…

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Q: f(x+h)-f(x) For f(x) = V3x + 13, find f '(x) using the definition f '(x) = lim f'(x) = Using this,…

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

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