微積分
極限、導數、最優化與函數性質。
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How to add and subtract fractions
Oh, fractions can be tricky at first but once you get the hang of it, it’s not so bad! The key thing is making sure the denominators (the bottom numbers) are the same. Like, if yo…
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find the compositions. $f(x) = 3x + 2, g(x) = x^2 - 4$ (a) $(f \\circ g…
\(3x^{2}-10\) ### Part (b)
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If point (3,-5) is on the graph of f(x) what point must be on the graph…
1. First blank: y-axis 2. Second blank: x-values 3. Third blank: y-values Filled sentence: Horizontal transformations reflect a function over the **y-axis**. Thus, they transform …
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7 to the power of 2
\(193\) ### Turn 2 Answer Got it, let's go through each one step by step using PEMDAS/BODMAS: 1) \(4 \times (2 \times 3 + 6^2) - 6\) - Inside parentheses: \(2×3=6\), \(6²=36\), so…
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the function $y = f(x)$ is graphed below. what is the average rate of c…
\(0\)
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number the answers
1. $2$ 2. $\frac{7}{3}$ or $2\frac{1}{3}$ 3. $\frac{20}{3}$ or $6\frac{2}{3}$ 4. $\frac{14}{3}$ or $4\frac{2}{3}$ 5. $2$ 6. $\frac{26}{11}$ or $2\frac{4}{11}$ 7. (Using problem 1)…
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question the graph of which of the following in the xy - plane does not…
\( y = \sqrt{x}+11 \) (the first option)
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sketch a graph of $f(x) = \\begin{cases} 2 & \\text{if } x \\leq -1 \\\…
The graph consists of: - A horizontal line segment at $y = 2$ for $x \leq -1$ (with a closed dot at $(-1, 2)$). - A line segment from $(-1, 2)$ (open dot, but the first segment ha…
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which decimal is equivalent to \\(\frac{5}{6}\\) ? \\(\\circ\\ 0.8\\bar…
\( 0.8\overline{3} \) (the first option: \( 0.8\overline{3} \))
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Which one
The first linear function (the leftmost table) has the largest y-intercept, which is 2. ### Turn 2 Answer Oops, did I overcomplicate it? Let me break it down super simply: 1. The …
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204 ÷ 0.6 =
340
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Can you please write that out for me
The quotient is 120 with a remainder of 17, or written as $\frac{9857}{82} = 120 + \frac{17}{82}$ ### Turn 2 Answer Absolutely! Let me walk through it step by step like you'd writ…
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Can you please write that out for me
The quotient is 61 and the remainder is 77. $4938 = 81 \times 61 + 77$ ### Turn 2 Answer Absolutely! Let me walk through it step by step like you’d do longhand: 61 ------ 81 | 493…
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Can you please write that out
The quotient is 36 with a remainder of 38, or approximately $36.57$ as a decimal. ### Turn 2 Answer Absolutely! Let me walk through it step by step like you'd do longhand: ``` 36 …
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Can you write that out
The quotient is 132 with a remainder of 13, or as a decimal approximately $132.19$, or as a fraction $\frac{9253}{70}$ ### Turn 2 Answer Got it, let's break this down super simply…
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Oki tysm i’ma send you another one now
630
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graph: $f(x) = -sqrt{x}$ step 1: evaluate the function to find three po…
The table is filled as above, and the graph is a curve passing through \((0,0)\), \((1,-1)\) and \((4,-2)\) with the domain \(x\geq0\) and decreasing for \(x\geq0\).
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kuta software - infinite calculus average rates of change for each prob…
\( 2 \) ### Problem 2: \( v = -\frac{1}{x - 2} \); \([-3, -2]\)
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kuta software - infinite calculus name_____________________________ ave…
2 ### Problem 2: \( v = -\frac{1}{x - 2} \); \([-3, -2]\)
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trazar la recta. $y = -\\frac{3}{2}x - 3$
To draw the line \(y =-\frac{3}{2}x-3\), plot the points \((0, - 3)\), \((2,-6)\) (or \((-2,0)\)) and draw a straight line through them.
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10 points - fill in each blank, table, & graph the following rational f…
Vertical asymptote: $\boldsymbol{x=-2}$ Horizontal asymptote: $\boldsymbol{y=1}$ x-intercept: $\boldsymbol{(-5, 0)}$ y-intercept: $\boldsymbol{(0, \frac{5}{2})}$ hole: $\boldsymbo…
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4) label the graphs with the correct functions. dashed: solid: a. $f(x)…
dashed: $\boldsymbol{g(x)=e^{3x}}$ solid: $\boldsymbol{f(x)=e^{2x}}$
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determine the zeros and the vertical intercept of the polynomial functi…
The zero(s) of the function is/are $x=8$ (multiplicity 2), $x=-6$, $x=11$ The horizontal intercept(s) is/are $(8, 0)$, $(-6, 0)$, $(11, 0)$ The vertical intercept is $(0, -8448)$ …
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approximate the area of the region bounded by $y = -\\frac{1}{4}x^{2}+9…
$\frac{26 + 34}{2} = 30$
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7) label the graphs with the correct functions. dotted: solid: a. $f(x)…
dotted: a. $f(x) = -2 \cdot 3^x$ solid: b. $g(x) = -3 \cdot 3^x$
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8) label the graphs with the correct functions. dashed: dotted: solid: …
dashed: a. \(f(x) = e^x\) dotted: c. \(h(x) = 2^x\) solid: b. \(g(x) = 3^x\)
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evaluate $int_{-8}^{0} (-sqrt{-x^{2}-8x})dx$
$-8\pi$
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question 4 (1 point) listen $2 \\cdot 3 + 10 \\div 2 = 8$ true false
False
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5 for which of the following functions does $f(2) = -1$? choose all tha…
A. $f(x)=3^{x}-10$, B. $f(x)=\frac{9}{4}x^{2}-10$
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question 5 (1 point) listen solve the following: $(7 + 41) \\div 2 - 15…
9
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use end behavior to select the correct function for each graph: a. $x^2…
Top (green) graph: d. $x^3 - 4x^2$ Second (red) graph: b. $-x^4 + 2x^2$ Third (orange) graph: a. $x^2 - 7x + 9$ Bottom (blue) graph: c. $-x^3 - x^2 + 2x - 3$
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use end behavior to select the correct function for each graph: a. $x^2…
Top (orange) graph: a. $x^2 - 8x + 9$ Second (green) graph: b. $x^3 - 4x^2$ Third (red) graph: d. $-x^4 + 2x^2$ Bottom (blue) graph: c. $-x^3 - x^2 + 4x - 3$
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which graphs are inverses of one another?○ graph a and b○ graph a and c…
none of the graphs shown
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19. is the inverse of the function $f(x) = -60(x - 3)^2 - 50$ also a fu…
No, the inverse of $f(x) = -60(x-3)^2 - 50$ is not a function. The original function is a downward-opening parabola, which fails the horizontal line test (horizontal lines interse…
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victoria invested $9,300 in an account paying an interest rate of 4.5% …
$12743.60$
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¿cuál es la pendiente de esta línea? pendiente indefinida pendiente cero
Pendiente cero
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4. $\\dfrac{3,200}{80}$
40
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which of the following is a rational function with horizontal asymptote…
A. $y = \frac{5x + 4}{x + 4}$
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multiple-choice question since slope is the change in the y values/chan…
*Note: There is a discrepancy between the calculated slope (-1) and the provided options. If following the marked $\Delta y=-2$, $\Delta x=+2$ from the table, the slope is $\bolds…
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2:22pm mon feb 9 m317 cs unit 5b rationals part 2 test s fill in the bl…
$x=5,x=-2$