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Pakistan
(a) \( 4 \times 2 \times 9=4 \times \square=\square \times 9 \) (b) \( 6 \times 3 \times 1=6 \times \square=\square \times 1 \) (c) \( 8 \times 7 \times 7=8 \times \square=\square \times 7 \)
Arithmetic Dec 02, 2024
a use the protractor to draw \( \begin{array}{llll}\text { a) } 35^{\circ} & \text { b) } 45^{\circ} & \text { c) } 240^{\circ}\end{array} \)
Geometry Dec 02, 2024
\( \int _ { - 1 } ^ { 3 } \int _ { x ^ { 2 } } ^ { 2 x + 3 } d y d x \)
Calculus Dec 02, 2024
\( A = \int _ { - 1 } ^ { 3 } x _ { x ^ { 2 } } ^ { 2 x + 3 } d y d x \)
Calculus Dec 02, 2024
Show that the function \( f(x)=|x-6| \) is not differentiable at 6 . Find a formula for \( f^{\prime} \) and sketch its graph. The left-hand and right-hand derivatives of \( f \) at \( a \) are defined by \[ f_{-}^{\prime}(a)=\lim _{h \rightarrow 0^{-}} \frac{f(a+h)-f(a)}{h} \] and \( f_{+}^{\prime}(a)=\lim _{h \rightarrow 0^{+}} \frac{f(a+h)-f(a)}{h} \) if these limits exist. Then \( f^{\prime}(a) \) exists if and only if these one-sided derivatives exist and are equal. (a) Find \( f_{-}^{\prime}(4) \) and \( f_{+}^{\prime}(4) \) for the function \[ f(x)=\left\{\begin{array}{ll}0 & \text { if } x \leqslant 0 \\ 5-x & \text { if } 0<x<4 \\ \frac{1}{5-x} & \text { if } x \geqslant 4\end{array}\right. \] (b) Sketch the graph of \( f \). \( \quad \) (c) Where is \( f \) discontinuous? (d) Where is \( f \) not differentiable?
Calculus Dec 01, 2024
\( 8 \times 9 - [ 32 - \{ 24 \div ( 8 - \overline { 4 - 2 } ) \} ] \)
Pre Algebra Dec 01, 2024
\( 8 \times 9 - [ 32 - \{ 24 \div ( 8 - \overline { 4 - 2 } ) \} ] \)
Pre Algebra Dec 01, 2024
1-6 Write the composite function in the form \( f(g(x)) \). [Identify the inner function \( u=g(x) \) and the outer function \( y=f(u) \). Then find the derivative \( d y / d x \) \( \begin{array}{ll}\text { 1. } y=\sqrt[3]{1+4 x} & \text { 2. } y=\left(2 x^{3}+5\right)^{4} \\ \text { 3. } y=\tan \pi x & \text { 4. } y=\sin (\cot x) \\ \text { 5. } y=e^{\sqrt{x}} & \text { 6. } y=\sqrt{2-e^{x}}\end{array} \$ \)
Calculus Dec 01, 2024
Q3. Chain Rule of Derivatives 1-6 Write the composite function in the form \( f(g(x)) \). [Identify the inner function \( u=g(x) \) and the outer function \( y=f(u) \).\( ] Then find the derivative d y / d x \) \( \begin{array}{ll}\text { 1. } y=\sqrt[3]{1+4 x} & \text { 2. } y=\left(2 x^{3}+5\right)^{4} \\ \text { 3. } y=\tan \pi x & \text { 4. } y=\sin (\cot x) \\ \text { 5. } y=e^{\sqrt{x}} & \text { 6. } y=\sqrt{2-e^{x}}\end{array} \)
Calculus Dec 01, 2024
1-6 Write the composite function in the form \( f(g(x)) \). [Identify the inner function \( u=g(x) \) and the outer function \( y=f(u) \).] Then find the derivative \( d y / d x \) \( \begin{array}{ll}\text { 1. } y=\sqrt[3]{1+4 x} & \text { 2. } y=\left(2 x^{3}+5\right)^{4} \\ \text { 3. } y=\tan \pi x & \text { 4. } y=\sin (\cot x) \\ \text { 5. } y=e^{\sqrt{x}} & \text { 6. } y=\sqrt{2-e^{x}}\end{array} \)
Calculus Dec 01, 2024
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